Localization system and associated method

ABSTRACT

A method for determining a localization parameter of an object includes generating a plurality of estimates of a first frequency-domain amplitude of a baseband signal from the object, each estimate corresponding one of a plurality of temporal segments of the baseband signal. The method also includes determining the first frequency-domain amplitude as most common value of the plurality of estimates, and determining the localization parameter therefrom. A localization system includes a memory and a microprocessor. The memory stores instructions and is configured to store a baseband signal having a temporal frequency component and a corresponding first frequency-domain amplitude. The microprocessor is adapted to execute the instructions to: (i) generate a plurality of estimates of the first frequency-domain amplitude each corresponding to a respective one of a plurality of temporal segments of the baseband signal, and (ii) determine the first frequency-domain amplitude as the most common value of the estimates.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a 35 U.S.C. § 371 filing of InternationalApplication No. PCT/US2016/068434, filed Dec. 22, 2016, which claimspriority to U.S. Provisional Application No. 62/387,387 filed Dec. 23,2015, which is incorporated by reference in its entirety. Thisapplication is also a continuation in part of U.S. patent applicationSer. No. 15/162,329 filed May 23, 2016, which claims priority to U.S.Provisional Application No. 62/164,696 filed May 21, 2015. Each of theabove-referenced applications is incorporated by reference herein in itsentirety.

BACKGROUND

A localization system tracks location and movement of one or moreobjects within a localization domain that are in the field of view ofthe localization system. An angle-based localization system determineslocations, in part, by computing relative angles between tracked objectsand a location on a plane. Angle-based localization systems are oftenpreferable to image-based localization systems, for example, when highlocalization precision is required and/or when the size of thelocalization domain far exceeds that of an image sensor of animage-based localization system.

SUMMARY OF THE INVENTION

In a first embodiment, a method for determining a localization parameterof an object includes generating a plurality of estimates of a firstfrequency-domain amplitude of a baseband signal from the object. Each ofthe plurality of estimates corresponds to a respective one of aplurality of temporal segments of the baseband signal. The firstfrequency-domain amplitude corresponds to a temporal frequency of thebaseband signal. The method also includes determining the firstfrequency-domain amplitude as most common value of the plurality ofestimates, and determining the localization parameter based on the firstfrequency-domain amplitude.

In a second embodiment, a localization system includes a memory and amicroprocessor. The memory stores non-transitory computer-readableinstructions and is configured to store a baseband signal having atemporal frequency component and a corresponding first frequency-domainamplitude. The microprocessor is adapted to execute the instructions to:(i) generate a plurality of estimates of the first frequency-domainamplitude each corresponding to a respective one of a plurality oftemporal segments of the baseband signal, and (ii) determine the firstfrequency-domain amplitude as the most common value of the plurality ofestimates.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows a localization system in an exemplary use scenario, in anembodiment.

FIG. 2 illustrates an embodiment of a localization system that is anexample of localization system of FIG. 1.

FIG. 3 is a perspective view of a localization system, which is anexample of the localization system of FIG. 2.

FIG. 4 is a cross-sectional view of the localization system of FIG. 3.

FIG. 5 includes plots of exemplary transmission functions of opticalmasks of the localization system of FIG. 3.

FIG. 6 is a flowchart illustrating a method for determining an angularlocation of an object, in an embodiment.

FIG. 7 is a flowchart illustrating optional steps of the method of FIG.6, in an embodiment.

FIG. 8 shows exemplary baseband signals from channels of thelocalization system of FIG. 2.

FIG. 9 shows a time series of short-time Fourier transform (STFT)amplitudes of the baseband signal of FIG. 8.

FIGS. 10A and 10B are plots of prediction errors corresponding to STFTamplitudes of FIG. 9.

FIGS. 11A and 11B are signal-to-noise ratio (SNR) time series of theprediction error of FIG. 10A.

FIG. 12 is a plot of a corrupted baseband signal generated by a channelof an embodiment of localization system of FIG. 2.

FIG. 13 illustrates a plurality of STFT amplitude estimatescorresponding to a respective plurality of segments of the corruptedbaseband signal of FIG. 12.

FIG. 14 depicts schematic histograms illustrating occurrences of STFTamplitude estimates of FIG. 13.

FIG. 15 is a flowchart illustrating a method for determining afrequency-domain amplitude of a baseband signal, in an embodiment.

FIGS. 16A and 16B are plots comparing raw STFT amplitude estimates andrefined STFT amplitude estimates resulting from the method of FIG. 15.

FIG. 17 is a time-series plot of measured STFT amplitudes generated byan embodiment of localization system of FIG. 2.

FIG. 18 shows histograms of the STFT amplitudes of FIG. 17 generated viathe method of FIG. 15.

FIGS. 19A and 19B are plots of prediction errors of the STFT amplitudesof FIG. 17.

FIG. 20 is a plot of a ratio of STFT amplitudes of FIG. 17.

FIG. 21 is a plot of a ratio of STFT amplitudes of FIG. 17 withcorrupted measurements excised.

FIG. 22 is a plot of signal-to-noise ratios corresponding to STFTamplitude ratios of FIGS. 20 and 21.

FIG. 23 illustrates an optical component array present in an embodimentof a receiver of the localization system of FIG. 2.

FIGS. 24-27 each illustrate a respective transmitter-receiver pair thatincludes the receiver of the localization system of FIG. 2.

FIGS. 28-32 each illustrate a wavefront traversing an embodiment ofreceiver that includes the optical component array of FIG. 23.

FIG. 33 illustrates one exemplary localization system, in an embodiment.

FIGS. 34-38 describe examples of exemplary uses of the localizationsystem of FIG. 2 and the method of FIG. 6.

FIG. 39 illustrates a first exemplary use environment for thelocalization system of FIG. 2, in an embodiment.

FIG. 40 illustrates a second exemplary use environment for thelocalization system of FIG. 2, in an embodiment.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1 shows a localization system 100 in an exemplary use scenariowithin an environment 180. Environment 180 is for example a warehouse, afactory, a fabrication plant, a job site, a construction site (for aroad, building, etc.), a landscaping site, and may be located eitherindoors or outdoors. The physical scale, electrical bandwidth, andrequired localization precision in this scenario are each sufficientlylarge as to make image-processing-based localization very difficultand/or resource intensive. Localization system 100 may include anyfeature of optical guidance systems 500, 600, and 700 described in U.S.application Ser. No. 14/165,946.

Environment 180 includes a vehicle 184, a person 186 wearing a vest186V, and obstructions, such as shelves 182, which limit a human'sline-of-sight ability. Vehicle 184 is for example a forklift or othertype of vehicle with a repositionable part, such as constructionequipment (backhoe, excavator, bulldozer, etc.). Localization system 100includes a receiver 130(1) and tracks positions of emitters 111, whichare on trackable objects such as vehicle 184, vest 186V, and shelves182. Receiver 130(1) has a front surface 130F(1) in a planeperpendicular to the x-y plane of a coordinate system 198. Localizationsystem 100 optionally includes one or more additional receivers, such asa second receiver 130(2).

In an embodiment, both receivers 130 and emitters 111 are located on asame vehicle, such as vehicle 184, for determining and controllinglocation of a moving part of vehicle 184.

Emitters 111 may be part of localization system 100. In an exemplarymode of operation, receiver 130(1) receives a signal 112(1) from emitter111(1), from which localization system 100 determines locationinformation about emitter 111(1).

One function of localization system 100 may be to localize and reportthe locations of objects or people, such as vehicle 184 and person 186.For example, localization system 100 determines a location angle 113 inthe x-y plane between emitter 111(1) and front surface 130F(1).Localization system 100 may also determine a second localization angleof emitter 111(1) with respect to receiver 130(2). Such location datamay be used to control object locations, such as vehicle 184, forpurposes of navigation and collision avoidance.

Receiver 130 may receive corrupted signals from emitters 111, e.g., fromemitter 111(2) emitting signal 112(2). For example, when an occlusion188 is between emitter 111(2) and receiver 130(2), receiver 130(2)receives a corrupted signal 112C, which is a corrupted version of signal112(2). Occlusion 188 is for example airborne dust, or ambient moisturein the form of rain, sleet, or snow. Corrupted signal 112C may also becaused by a malfunction of an emitter 111. Reliable operation oflocalization system 100 requires system 100 be able to remove noise incorrupted signal 112C such that it can accurately locate emitter 111(2).

FIG. 2 illustrates one exemplary localization system 200, which is anexample of localization system 100. Localization system 200 includes areceiver 230 and optionally a processing unit 280. Processing unit 280includes a microprocessor 282 and a memory 284. Memory 284 may representone or both of volatile memory (e.g., SRAM, DRAM, or any combinationthereof) and nonvolatile memory (e.g., FLASH, ROM, magnetic media,optical media, or any combination thereof). Memory 284 stores software250 that includes machine-readable instructions. Microprocessor 282 iscommunicatively coupled to memory 284 and, when executing themachine-readable instructions stored therein, performs functions oflocalization system 200 as described herein. Software 250 includes aspot-location estimator 252, a position-to-angle converter 254, andoptionally a frequency domain analyzer 256, a signal conditioner 258, asignal evaluator 260, a signal-to-noise (SNR) monitor 262. Memory 284may also store mask properties 234P, CRA mapping 235M, and time interval264 that are optionally used by spot-location estimator 252,position-to-angle converter 254, and SNR monitor 262, respectively.

Localization system 200 may also include optional emitters 211. Receiver230 and emitters 211 may be implemented as receiver 130(1) and emitters111, respectively. Emitters 211 include at least emitter 211(1) and mayfurther include any number of emitters 211(2) through 211(N). Eachemitter 211(1-N) provides a respective optical signal 212(1-N) having acarrier frequency 212C. Optical signals 212(1-N) may have modulationfrequency 212F(1-N) and a corresponding frequency-domain amplitude212A(1-N), in which case carrier frequency 212C is a carrier frequency.In a typical use scenario, localization system 200 is in an environmentthat includes ambient optical radiation 218 that includes carrierfrequency 212C in its optical spectrum. Modulation frequencies 212F ofoptical signals 212 enable localization system 200 to distinguish asignal propagating from emitters 211 from the component of ambientoptical radiation 218 having carrier frequency 212C.

Emitter 211 may include a light source 215, such as a light-emittingdiode (LED) or laser diode, which generates optical signal 212. Anemitter 211 may also include electrical circuitry 215C configured tomodulate output of light source 215. Optical signal 212 may beoriginally generated by a source distant from an emitter 211, such as anoptical transmitter 220, which is for example part of localizationsystem 200 and may be attached to or proximate receiver 230. Emitter 211may include a reflector 216 for reflecting optical signal 212 generatedby optical transmitter 220 toward receiver 230. Optical transmitter 220may emit electromagnetic radiation such as visible light, near-infraredlight, and a combination thereof.

Modulating optical signals 212(1-N) with a respective modulationfrequency 212F(1-N) is one way to distinguish emitters 211 from oneanother. Alternatively, each emitter 211 may emit a different carrierfrequency (212C(1, 2, . . . N)) or polarization. A channel 231 mayinclude a filter 236 for transmitting a carrier frequency 212C orpolarization corresponding to that of light propagating from a singleemitter 211. Filter 236 includes, for example, at least one of anoptical bandpass filter, a linear polarizer, and a circular polarizer.

Carrier frequency 212C corresponds, for example, to one or morefree-space optical wavelengths between 0.40 μm and 2.0 μm, such as0.95-μm. Filter 236 is for example a narrow-band optical bandpass filterhaving a center transmission frequency equal to carrier frequency 212C.Modulation frequencies 212F are for example between 50 Hz and 500 kHz.Optical signals 212 may be modulated with one or more modulation methodsknown in the art, which include amplitude modulation, frequencymodulation, spread-spectrum, and random one-time code modulation.

Receiver 230 includes a plurality of channels 231. Each channel 231includes an optical mask 234, a photodetector 233, channel electronics232, and optionally a lens 235. Each optical mask 234 is between itsrespective photodetector 233 and emitter 211 such that optical signals212 propagate through an optical mask 234 before being detected by aphotodetector 233 therebehind. Two or more optical masks 234(1-M) may bedistinct optical elements. Alternatively, two or more optical masks234(1-M) may correspond to a different region of a single opticalelement that covers two or more respective photodetectors 233.

In an embodiment, each photodetector 233 is a single-pixelphotodetector, for example a photodiode such as a silicon PIN diode thathas, for example, a temporal cut-off frequency of 20 MHz. In anotherembodiment, photodetectors 233 are implemented in a pixel array suchthat each photodetectors 233 is a different pixel of the pixel array.The pixel array is, for example, a complementarymetal-oxide-semiconductor (CMOS) image sensor or a charge-coupled device(CCD) image sensor.

Channels 231 may be arranged in any spatial configuration withinreceiver 230. In one embodiment, channels 231 are arranged along a line.In another embodiment, channels 231 are arranged within a plane but notall lie on the same line, such that channels 231 define a plane. Forexample, channels 231 are arranged in a two-dimensional array.

Each optical mask 234(1-M) is mutually distinct, such that optical mask234(m) of channel 231(m) differs from optical mask 234(n) of channel231(n), where m≠n. Without departing from the scope hereof, receiver 230may also include, in addition to channels 231(1-M), additional channels231 having an optical mask 234 identical to an optical mask 234 of achannel 231(1-M),

Optical masks 234 may impose a respective signal modification ofincident optical signals 212. The signal modification is at least one ofa change in phase, amplitude, or polarization, and is for examplefunctionally or numerically representable as a mask property 234Poptionally stored in memory 284. An optical mask is for example anoptical element with a spatially-varying transmissivity described by aspatially-varying transmission function, which is an example of a maskproperty 234P stored in memory 284. Mask property 234P is, for example,a look-up table representing the transmission function. Each opticalmask 234 modifies the optical signal 212 transmitted therethrough tophotodetector 233 and hence, with the exception of a phase-only mask,also modifies frequency-domain amplitude 212A corresponding to opticalsignal 212.

Optical signals 212(1-N) are incident on channels 231 at respectivelocation angles 213(1-N), illustrated in FIG. 2 as a single angle forclarity of illustration. Each location angles 213 is an example oflocation angle 113. When included in a channel 231(i), where i∈{1, 2, .. . , M}, lens 235 is between the channel's photodetector 233(i) and anemitter 211(i) such that lens 235 maps angle 213 to an signal location291 on photodetector 233(i) upon which optical signal 212 is incident.

Location angle 213 is for example a chief-ray angle (CRA) of a ray (thechief ray) incident on lens 235. Lens 235 maps angle 213 to an signallocation 291 according to a characteristic CRA function, which may bestored in memory 284 as CRA mapping 235M. CRA mapping 235M is forexample a lookup table of chief-ray angles and corresponding signallocations 291. CRA mapping 235M may also include properties of lens 235such as its focal length and distance from optical mask 234.

Each channel 231 has a respective channel field of view (“channel-FOV”)by virtue of the size of its photodetector and, when included, therelative aperture (f-number) of lens 235. In an embodiment, channel-FOVsof three or more channels 231 overlap such that at least three channels231 receive optical signal 212 from a same emitter 211.

Each optical mask 234 transmits one or more optical signals 212(1-N) tophotodetector 233 as a modified optical signal 212M, which in turngenerates a photocurrent signal 233C received by channel electronics232. For example, photodetectors 233 of channel 231(1) generatesphotocurrent signal 233C(1).

Channel electronics 232 may include circuitry capable of performing oneor more of the following operations on photocurrent signal 233C:analog-to-digital conversion, low-pass filtering, and a demodulation.For example, channel electronics 232 includes low-pass filter circuitrythat also functions as an analog demodulator. In another example,channel electronics 232 includes a low-pass filter, an analog-to-digitalconvertor, and a digital demodulator.

In an embodiment, channel electronics 232 of one or more channels 231 iscapable of demodulating photocurrent signal 233C to recover, if present,more than one modulation frequency 212F. For example, within ademodulation period T, channel electronics 232 demodulates photocurrentsignal 233C at a demodulation frequency equal to one of 212F(1-N₁) for aduration T/N₁, where 1<N₁≤N. In an embodiment, one or more channels 231has dedicated channel electronics 232 corresponding to a singlemodulation frequency 212F. In another embodiment, channel electronics232 provides amplification and is spatially separate from, wheredemodulation, filtering and digital conversion occurs, e.g., withinprocessing unit 280 to which channel electronics 232 is communicativelycoupled. In this embodiment, channel electronics 232 may also providebias cancellation.

Channel electronics 232 of each channel 231(m) outputs a respectivechannel signal 231S(m) to memory 284 communicatively coupled tomicroprocessor 282, where m∈{1, 2, . . . , M}. Each channel signal231S(m) includes a measured signal amplitude 241(m), which may be storedas a measured signal amplitude 242 in memory 284. Measured signalamplitude 241(m) may be the amplitude of channel signal 231S(m), forexample, when optical signal 212 is not modulated, or prior todemodulation, filtering, and digital conversion of channel signal231S(m).

When optical signal 212 is modulated, that is, with a modulationfrequency 212F(n) at a corresponding frequency-domain amplitude 212A(n),software 250 may determine measured signal amplitude 242(n, m)corresponding to optical signal 212(n) as detected by channel 231(m),where n∈{1, 2, . . . , N}.

Microprocessor 282 may include circuitry configured to and capable ofperforming one or more of the following operations on photocurrentsignal 233C: amplification, analog-to-digital conversion, low-passfiltering, and a demodulation. For example, microprocessor 282 andchannel electronics 232 are complementary, such that at least one ofthem performs amplification, analog-to-digital conversion, low-passfiltering, and a demodulation on the respective signals they receive.

In one embodiment, microprocessor 282 is integrated with receiver 230.For example, microprocessor 282 and receiver 230 may be located on thesame circuit board. Microprocessor 282 may be integrated into a channel231, which then functions as a master with other channels 231 beingslaves. In another embodiment, microprocessor 282 is separate fromreceiver 230. For example, microprocessor 282 and receiver 230 share anenclosure, or microprocessor 282 is located on a separate computer at adistance away from receiver 230. Localization system 200 may includemore than one receiver 230, which may be communicatively coupled andindependently positionable with respect to microprocessor 282 and memory284.

In an embodiment, localization system 200 measures location angles213(1-N) corresponding to respective emitters 211(1-N), which may bestored in memory 284 as measured location angles 213M(1-N). Measuredlocation angles 213M(1-N) correspond to a respective location angle213(1-N). Localization may be configured to output localization data209, such as angles 213M, to a controller 270, via wired or wirelesscommunication. Controller 270 may be remotely located such that itreceives localization data 209 via a computer network 272, which is forexample an intranet or the Internet. Localization system 200 may also beconfigured to receive instructions 274 from controller 270 and transmitthem, via a control transmitter 266, to a receiver 217 on an object thatalso includes an emitter 211. For example, emitter 211(N) may includereceiver 217, and is an example of emitter 111(1) on vehicle 184.Alternatively, a receiver 217 need not be integrated (co-packaged) withan emitter 211, such that an object such as vehicle 184 may include areceiver 217 and emitter 211 that are independently positionable.Control transmitter 266 and receiver 217 are WiFi, Bluetooth, BluetoothLow Energy (BLE), Cellular (3G, 4G, 5G, LTE, LTE-U, NB-1, CAT,etc.)-compliant devices, for example, but may be any wirelesstransmission protocol without departing from the scope hereof.

FIG. 3 is a perspective view and FIG. 4 is a cross-sectional view of alocalization system 300. FIGS. 3 and 4 are best viewed together in thefollowing description. FIG. 3 includes a coordinate system 398 that hasan x-y plane, an x-z plane, and a y-z plane. Herein, references to x, y,and z directions (or axes) and planes formed thereof are of coordinatesystem 398, unless otherwise specified. Localization system 300 is anexample of localization system 200 and includes channels 331(1-3),channel electronics 432, microprocessor 282, and memory 484.

Channels 331(1-3) are each examples of channels 231 and includephotodetectors 333(1-3), optical masks 334(1-3), and lenses 335(1-3),respectively. Photodetectors 333, optical masks 334, and lenses 335 areexamples of photodetectors 233, optical masks 234, and lenses 235,respectively. Channel electronics 432 is an example of channelelectronics 232. Memory 484 is an example of memory 284 and includesmask properties 334P of masks 334 and CRA mapping 335M of lenses 335.Mask properties 334P and CRA mapping 335M are examples of maskproperties 234P and CRA mapping 235M, respectively.

The relative positions of channels 331 may change without affecting thefunctionality of localization system 300. For example, channel 331(1)may be between channels 331(2,3), or channel 331(3) may be betweenchannels 331(1,2).

Optical masks 334(1-3) span a region in the x-direction between x_(min)and x_(max), where distance (x_(max)-x_(min)) is, for example, equal toa width 333 W of each photodetector 333 or an image circle from lenses335, either of which may also span the region. Distance(x_(max)-x_(min)) may be less than or exceed width 333 W withoutdeparting from the scope hereof. Each optical mask 334 is in a planeparallel to the x-y plane that is perpendicular to a plane 396, which isparallel to the x-z plane. Lenses 335 are in front of optical masks334(1-3) and have respective optical axes 335A(1-3) that are coplanar ina plane 397, which is orthogonal to plane 396. The cross-sectional viewof FIG. 4 represents a cross-sectional view of localization system 300in plane 396, or in a plane parallel to plane 396 that includes one ofoptical axes 335A(1) and 335A(3).

Optical masks 334(1-3) are each part of a respective channel 331(1-3) oflocalization system 300 that have respective fields of view that overlapin a region that includes an object 391. Object 391 has thereon anemitter 311 that intersects plane 396. Emitter 311 is an example ofemitter 211. Line 395 is in plane 396 and is perpendicular to the x-yplane. Line 395 is for example collinear with an optical axis 335A oflens 335 in front of optical mask 334(2). Optical mask 334(2) may be abiplanar absorptive filter (with gradient transmissivity) or awedge-shaped absorption filter having a thickness that varies in the xdirection. Channels 331 span a range 394 of y-coordinate values. Object391 and emitter 311 are shown within this range for illustrativepurposes only, and may be outside of this range without departing fromthe scope hereof.

In plane 396, emitter 311 is located at a distance 311D fromphotodetector 333(2), a distance 311 z from a plane that includesphotodetectors 333, and a distance 311 x from plane 397. Distances 311 xand 311 z correspond to emitter 211 having a location angle 313 withrespect to plane 397, or equivalently with respect to optical axis335A(2). Location angle 313 is an example of angle 213, and herein isalso referred to as location angle θ.

Channels 331(1-3) are arranged collinearly in the y-direction. Forexample, channels 331(1-3) are center-aligned in the x-direction suchthat each optical axis 335A(1-3) is in plane 397. Such center alignmentprevents parallax-induced errors in determining angle 313. For example,if channels 331 were translated along the negative y-direction such thatoptical axis 335A(1) of channel 331(1) were in plane 397, the anglebetween emitter 311 and optical axis 335A(1) equals aforementionedlocation angle 313 only if channels 331(1-2) are center-aligned in thex-direction. In another embodiment, the parallax effect is used as aranging estimator by purposefully arranging channels to induce parallaxerrors.

Photodetectors 333 are separated by a center-to-center distance 333Salong the y direction. Distance 333S is for example between onemillimeter and ten centimeters, which is much less than a typicaldistance 311D.

Lenses 335 have a focal length ƒ and are located a distance 434D fromrespective optical masks 334. Distance 434D for example equals focallength ƒ±Δ, where defocus distance Δ may equal zero. Emitter 211 emitsoptical signal 312, which is an example of optical signal 212. Opticalsignal 312 includes a chief ray 412(0) and marginal rays 412(±1), whichlens 335 images onto an image plane 335P. Rays 412 form a spot 422 atoptical mask 334 that has a spot size 422D. Spot size 422D may be afull-width-half-max spot size or a 1/e² spot size. Spot 422 is centeredat a signal location 491 x with respect to plane 397.

Image plane 335P is, for example, within optical mask 334, at a frontsurface or back surface thereof, or between optical mask 334 andphotodetector 333. Optical mask transmits optical signal 312 as amodified optical signal 412M, which is an example of modified opticalsignal 212M.

In some embodiments, it is advantageous for the lens 335 to produce alarge spot (e.g., a minimum spot size relative to the diffraction limit)or for image plane 335P to be displaced from optical mask 334 (|Δ|>0)such that spot 422 is either large by design or a blurred spot onoptical mask 334. Lens 335 may be designed to yield a large optical spotto enable misfocus invariance, such as for extended depth of field, wideFOV, chromatic aberration control and/or thermal control. Another way toform a large optical spot is through simple misfocus.

For example, optical mask 334 has a spatially-varying transmissivitythat is binary (transmission equals either T_(min) or T_(max)) andperiodic in the x direction with a period Λ_(x). Period Λ_(x) is betweentwenty-five micrometers and fifty micrometers, for example. If spot size422D is less than period Λ_(x), then optical mask 334 may eithercompletely attenuate or completely transmit optical signal 312, whichwould result in processing unit being incapable of determining providinglocalization information about emitter 311 from modified optical signal412M. To avoid such a scenario, lens 335 may be designed to produce aspot at image plane 335P that has a spot size, as a function ofchief-ray angles χ, that minimally differs from period Λ_(x) forchief-ray angles χ within the field of view of channel 331.

In an embodiment, lens 335 has an f-number N=4, such that at free-spacewavelength λ₀=1.0 μm, its diffraction limited spot size (Airy diskdiameter) is approximately ten micrometers. Lens 335 may be designed todirect light to a spot having a minimum diameter that exceeds thediffraction limit. For example, the minimum diameter equals periodΛ_(x), with exemplary ranges described above.

Chief-ray 412(0) intersects optical axis 335A at chief-ray angle (CRA) χsuch that signal location 491 x equals (ƒ±Δ)tan(χ). Signal location 491x is an example of signal location 291, FIG. 2. In practice, chief-rayangle χ is approximately equal to location angle 313 (θ), which can beseen in FIG. 4. Location angle θ satisfies

${{\tan\;\theta} = \frac{411\; x}{411\; z}},$while chief-ray angle χ satisfies

${\tan\;\chi} = {\frac{{411\; x} + {491\; x}}{411\; z}.}$In practice, distance 311 x is far greater than signal location 491 x,such that χ≅θ. Detector 333 may be a single-pixel detector for examplehas width 333W between one-half millimeter and ten millimeters such thatsignal location 491 x is less than five millimeters. By contrast,distance 311 x may be on the order of meters.

Chief-ray angle χ satisfies CRA mapping 335M relating chief-ray angle χand signal location 491 x. When lens 335 is a thin lens, CRA mapping335M is

${\tan\;\chi} = {\frac{491\; x}{434\; D}.}$Distance 434D is known, and hence determining signal location 491 xenables determination of chief-ray angle χ, and hence location angle θof emitter 311 and object 391.

Without departing from the scope hereof, chief-ray angle χ and signallocation 491 x may satisfy a relation other than

${{\tan\;\chi} = \frac{491\; x}{434\; D}},$for example, when lens 335 is a compound lens. In such a case, afunctional relationship or a numerical one-to-one mapping betweenchief-ray angle χ and signal location 491 x may be determined using lensdesign software known in the art and stored as CRA mapping 335M. Forexample, lenses 335 are image-side telecentric lenses, which decreasethe spatial dimensions, such as width 333W, of optical masks 334 andphotodetectors 333 sufficient for rays 412 to reach optical masks 334and photodetectors 333.

FIG. 5 includes plots 510,520, and 530 showing respective exemplarytransmission functions 334T(1-3) of optical masks 334(1-3). Opticalmasks 334 are for example formed of molded plastic or may be a clearopening for a unity transmission function. Optical masks 334 may includean absorbing dye at predetermined locations such that their transmissionfunctions 334T apply at a wavelength corresponding to carrier frequency212C. The absorbing dye absorbs near-infrared light, for example, andmay have a peak absorption at 950±20 nm. Any of optical masks 334(1-3)may have a plurality of opaque or transparent halftone shapes (dots,polygons, lines, etc.) arranged such that transmission functions334T(1-3) represent their respective measured transmission functions.Such a transmission function measurement employs an optical spot thatspans several halftone shapes such that the halftones yield an effectivespatial transmission gradient.

Transmission functions 334T(1-3) are each a function of a normalizedsignal location x_(norm) in a direction parallel to the x-dimension.Herein, transmission functions 334T(1-3) are also referred to asT₁(x_(norm)), T₂(x_(norm)), and T₃(x_(norm)) respectively. Transmissionfunctions 334T(1-3) may be independent of y, such that any spatialvariation thereof is entirely along the x direction. A 2D search may beperformed to isolate or determine the x and y spatial variation.Normalized signal location x_(norm) is between x_(min) and x_(max) ofFIGS. 3 and 4, for example.

Transmission function 334T(1) has a uniform transmission, in bothdirections x and y, equal to T_(max1), which is for example unity or0.99. Transmission function 334T(2) has a maximum T_(max2)≤T_(max1) anda minimum T_(min2)>0. Transmission function 334T(3) has a maximumT_(max3)≤T_(max1) and a minimum T_(min3)>0. Minimum transmissionsT_(min2) and T_(min3) are for example 0.20. Transmission functions334T(1-3) are each examples of a mask property 234P that may be storedin memory 484, as a lookup table for example.

Normalized signal location x_(norm) is normalized to a width of opticalmask 334 along the x-dimension. In response to modified optical signal412M, photodetectors 333(1-3) generate a respective photocurrent signal433C(1-3), which are each examples of photocurrent signal 233C, fromwhich channel electronics 432 generates respective channel signals431S(1-3) (FIG. 4). Channel signals 431S(1-3) are examples of channelsignals 231S.

The amplitude of channel signals 431S(1-3) may be stored in memory 284as measured signal amplitudes 242. The amplitude of channel signals431S(1-3) may correspond to a single modulation frequency amplitude212A, e.g., a frequency of amplitude modulation, of modified opticalsignal 412M that distinguishes signals from emitter 311 from ambientlight incident on channels 331. Alternatively, amplitudes of channelsignals 431S(1-3) may be proportional to respective photocurrent signals433C(1-3).

Herein, channel signals 431S(1-3) are also denoted by I₁, I₂, and I₃,respectively. Modified optical signal 412M has an optical power P₀,which can be considered uniform across photodetectors 333 becausedistance 333S between adjacent photodetectors 333 is small compared todistance 311D.

Channel signals I₁,I₂, and I₃ are proportional to the product of opticalpower P₀ and their respective transmission functions T₁, T₂, and T₃(m=1,2, or 3), as shown in Equation 1.I _(m) ∝T _(m) P ₀  Eq. (1)

Plots 510, 520, and 530 each denote a normalized signal location 591,which corresponds to signal location 491 x of FIG. 5. The value ofsignal location 591, that is, a value of x_(norm) between zero and one,may be determined given known transmission functions T₁, T₂, and T₃.

Channel 331(1) generates channel signal I₁ generated by photodetector333(1) that is independent of signal location 591 becauseT₁(x_(norm))=T_(max). Hence, on its own, the response of photodetector333(1), which is channel signal I₁, provides no information about signallocation 491 x, and accordingly no information about location angle 313.

Channel signal I₂ generated by channel 331(2) provides a coarse estimatex₂ of signal location 491 x because the functional form T₂(x_(norm)) isknown. In the example of plot 500(2), transmission function 334T(2)(T₂(x_(norm))) is represented by Equation 2, where T_(max2) and T_(min2)of optical mask 334(2) are known.T ₂(x _(norm))=T _(max2)−(T _(max2) −T _(min2))x _(norm)  Eq. (2)

Measured channel signals I₁ and I₂ provide a value of a ratio α₂=I₂/I₁.Ratio α₂ also equals T₂/T₁ because I₂∝T₂P₀, per Eq. 1. Hence, in channel331(2) signal location 591 corresponds to a transmission value ofT₂(x₂)=α₂T_(max1). Accordingly, α₂T₁, or equivalently α₂T_(max1), may besubstituted for T₂(x_(norm)) in Eq. 2, such that a first estimate x₂ ofx_(norm) can be determined from known quantities T_(max1), T_(max2), andT_(min2), as shown in Equation 3. Spot-location estimator 252 maydetermine first estimate x₂.

$\begin{matrix}{x_{2} = \frac{T_{\max\; 2} - {\alpha_{2}T_{\max\; 1}}}{( {T_{\max\; 2} - T_{\min\; 2}} )}} & {{Eq}.\mspace{14mu}(3)}\end{matrix}$

Transmission function 334T(2) is shown as linear in FIG. 5 and Eq. 2,but may be non-linear without departing from the scope hereof. Forexample, Transmission function 334T(2) may be a monotonically increasingor monotonically decreasing function of x_(norm), such as curves 522 and524. The above-mentioned examples of transmission function 334T(2) areeach a one-to-one function (a.k.a. an “injective” or “strictlymonotonic” function, to use mathematical terms), such that eachtransmission value between T_(min) and T_(max) corresponds to one andonly one value of x_(norm). A strictly monotonic function may be eitherstrictly increasing or strictly decreasing. Mathematically, transmissionfunction 334T(2) as shown in plot 520 is a strictly decreasing functionof increasing x_(norm) because it is always decreasing, rather thanincreasing or remaining constant. The injective or strictly monotonicproperty of transmission function 334T(2) enables measured photocurrentsignal 433C(2) (also denoted I₂) to identify a one (and only one) x₂value as an estimate of signal location 591. Herein, an optical maskwith an injective (strictly monotonic) transmission function (e.g.,strictly increasing or strictly decreasing) is called a slow-varyingoptical mask.

Different embodiments of optical mask 334(2) may have a same measuredtransmission function similar to transmission function 334T(2) shown inplot 520. In a first embodiment, optical mask 334(2) has a trulygradient transmission function. In a second embodiment, optical mask334(2) is a halftone mask. In a third embodiment, optical mask 334(2)has a plurality of gray levels equivalent to a step-wise approximationof transmission function 334T(2) such that, when its transmission ismeasured with an optical beam having a width wider than a step width,its measured transmission function is approximates or isindistinguishable from transmission function 334T(2). The step-wiseapproximation of an optical mask 334(2) may have just one step, suchthat it has two transmission values, 0.75 and 0.25, for example,indicating respectively a “left-half” or “right half” of optical mask334(2) in a direction parallel to the x_(norm) axis.

The accuracy of x₂ depends in part on an uncertainty ΔI₂ of channelsignal I₂, as ratio α₂=I₂/I₁. Since ratio α₂ also equals T₂/T₁, thisuncertainty may be represented in plot 520. Uncertainty ΔI₂ correspondsto an uncertainty Δx₂ of x₂, the magnitude of which is determined byslope

${\frac{{dT}_{2}}{{dx}_{norm}} = {\frac{( {T_{\max\; 2} - T_{\min\; 2}} )}{1}\mspace{14mu}{of}\mspace{14mu}{T_{2}( x_{norm} )}}},$as shown in Equation 4.

$\begin{matrix}{{\Delta\; x_{2}} = \frac{\Delta\; T_{2}}{( {{dT}_{2}/{dx}_{norm}} )}} & {{Eq}.\mspace{14mu}(4)}\end{matrix}$

Uncertainty Δx₂ can be reduced by increasing (T_(max2)−T_(min2)).However, as T_(min) approaches zero, measurements of modified opticalsignal 412M so attenuated become more noisy, such that ΔI₂ increases,and hence places a lower limit on uncertainty Δx₂.

Uncertainty Δx₂ may be reduced detecting optical power P₀ with a channelhaving an optical mask having a slope larger than (T_(max2)−T_(min2)).For example, channel 331(3) that has optical mask 334(3), which has atransmission function 334T(3), or T₃(x_(norm)), which in this example isperiodic. Transmission function 334T(3) may be a continuous function ofy, e.g., sinusoidal function, or a discontinuous function of y, e.g., asignum function of a periodic function (e.g., a square-wave function), atriangle function, or a sawtooth function.

Channel signal I₃ generated by photodetector 333(3) provides a refinedestimate x₃ of signal location 491 x because the functional formT₃(x_(norm)) is known. For example, T₃(x_(norm)) may be represented byEquation 5, where plot 520 illustrates period Λ_(x)divided by W_(x),which is photodetector width 333W.

$\begin{matrix}{{T_{3}( x_{norm} )} = {T_{\min} + {( {T_{\max} - T_{\min}} ){\sin( \frac{2\pi\; x_{norm}}{( {\Lambda_{x}/W_{x}} )} )}}}} & {{Eq}.\mspace{14mu}(5)}\end{matrix}$

Channel signals I₁ and I₃ provide a value of a ratio α₃=I₃/I₁. Ratio α₃also equals T₃/T₁ because I₃∝T₃P₀, per Eq. 1. Hence, in channel 331(3)signal location 591 corresponds to a transmission value ofT₃(x_(norm))=α₃T_(max), which is satisfied at several candidatelocations 532, denoted by dashed vertical lines in plot 530, because, inthe example of plot 530, T₃(x_(norm)) is a sinusoidal function. Onelocation 532 corresponds to signal location 591, which has the samevalue on each channel 331(1-3). Hence, the “correct” candidate location532 is the one closest to location x₂ determined for channel 331(2),denoted by normalized location 532(11) in plot 530. Normalized location532(11) may be considered a refined estimate of signal location 591, andhereinafter is also referred to a refined estimate 532(11) or refinedestimate x₃. Spot-location estimator 252 may determine refined estimate532(11).

Transmission function 334T(3) may be non-sinusoidal periodic function,such as a triangle waveform, without departing from the scope hereof.Transmission function 334T(3) may be also a non-injective andnon-periodic function, such as a quasi-periodic function or alocally-periodic function, without departing from the scope hereof.T₃(x_(norm)) of Eq. 5 can be generalized to represent a locally periodicfunction by specifying that period Λ_(x) is a function of x_(norm), thatis, Λ_(x)=Λ_(x)(x_(norm)).

In an embodiment, localization system 300 includes additional channels331 with respective optical masks 334 having a respective periodictransmission function identical to transmission function 334T(3), exceptthat they are shifted by a respective fraction of period Λ_(x)/W_(x).Transmission function 534T illustrates such a transmission function.Such an embodiment of localization system 300 may include three channels331, hereinafter “phase-shifted channels,” with respective transmissionfunctions 534T that are phase-shifted versions transmission function334T(3), where the respective phase shifts are 60°, 120°, and 180°. Suchan embodiment of localization system 300 may include two phase-shiftedchannels 331, with respective transmission functions 534T that arephase-shifted versions transmission function 334T(3), where therespective phase shift is 90°.

Such phase-shifted channels each provide additional sets of candidatelocations 532 such that refined estimate x₃ is determined from morecandidates, which enables refined estimate x₃ to be closer to coarseestimate x₂ than with fewer candidate locations 532. A second benefit ofphase-shifted channels becomes apparent when candidate locations 532 areat or near regions of transmission function 334T(3) have zero or verysmall slope, which results in large uncertainties as illustrated by Eq.4. A phase-shifted transmission function (e.g., function 534T) hascandidate locations in high-slope regions, and hence provide refinedestimates with low uncertainty.

The forgoing describes how localization system may operate to determine,for emitter 311, location angle 313 in plane 396. Localization system300 may also include additional channels 331′(2) and 331′(3), whichenable localization system 300 to determine for emitter 311, a secondlocation angle in plane 397, which is orthogonal to plane 396. Distance333S′ between channels 331′(3) and channel 331(1) is not to scale and isfor example equal to distance 333S. Channels 331′(2) and 331′(3) arecollinear to and in a plane parallel to channel 331(1). For example,channels 331(1), 331′(2), and 331′(3) are center-aligned along the ydirection and have lenses 335 with respective optical axes that arecoplanar in a plane parallel to plane 396. Channels 331′(2) and 331′(3)are equivalent to channels 331(2) and 331(3), but have respectiveoptical masks 334′(2) and 334′(3) rotated by ninety degrees with respectto optical masks 334(2) and 334(3) such their transmission varies alongthe x dimension. Channels 331(1), 331′(2), and 331′(3) would enablelocalization system to determine a second angular location of emitter311 in a plane parallel to plane 397.

FIG. 6 is a flowchart illustrating a method 600 for determining alocalization parameter of an object. Method 600 is for exampleimplemented by localization system 200 executing computer-readableinstructions of software 250. Localization parameters include eachposition relative to a rectangular coordinate system (x, y, z), aspherical coordinate system (radial distance r, azimuthal angle θ, andpolar angle φ), and Euler angles indicating rotational orientationrelative to a coordinate system: pitch, yaw, and roll. Angle 213M may beeither a azimuthal angle θ or a polar angle φ. The localizationparameter is, for example, an angular location such as measured locationangle 213M. The localization parameter may be a distance between theobject and a receiver that detects an electromagnetic signal propagatingfrom the object, e.g., in ranging applications.

In step 610, method 600 detects a first portion of an optical signalfrom the object. In an example of step 610, a first portion of opticalsignal 312 is incident on lens 335(1), which directs the first portiontoward detector 333(1).

Step 610 optionally includes step 612. In step 612, method 600 detectsthe first portion, the first portion having propagated through a uniformoptical mask having a uniform transmissivity that equals or exceeds amaximum transmissivity of a second optical mask. In an example of step612, lens 335(1) directs the first portion toward optical mask 334(1)such that the first portion propagates through optical mask 334(1)before being detected by detector 333(1).

In step 615, method 600 determines a first signal amplitude of thedetected first portion. In an example of step 615, channel electronics432 generates channel signal 431S(1) from photocurrent signal 433C,where the amplitude of channel signal 431S(1) is an example of the firstsignal amplitude.

In step 620, method 600 detects a second portion of the optical signaltransmitted through a slow-varying optical mask having a strictlymonotonic transmissivity T₂(x), in an x-range of a spatial dimension x.In an example of step 620, a second portion of optical signal 312 isincident on lens 335(2), which directs the second portion toward opticalmask 334(2).

In step 625, method 600 determines a second signal amplitude of thedetected second portion transmitted through the slow-varying opticalmask. In an example of step 625, channel electronics 432 generateschannel signal 431S(2) from photocurrent signal 433C, where theamplitude of channel signal 431S(2) is an example of the second signalamplitude.

In step 630, method 600 detects a third portion of the optical signaltransmitted through a fast-varying optical mask having aspatially-varying transmissivity T₃(x) having a same value at more thanone value of x in the x-range. In an example of step 630, a thirdportion of optical signal 312 is incident on lens 335(3), which directsthe third portion toward optical mask 334(3).

In step 635, method 600 determines a third signal amplitude of thedetected third portion transmitted through the fast-varying opticalmask. In an example of step 635, channel electronics 432 generateschannel signal 431S(3) from photocurrent signal 433C, where theamplitude of channel signal 431S(3) is an example of the third signalamplitude.

In step 640, method 600 determines a coarse-estimate location x₂ in thex-range and corresponding to a location on the slow-varying optical maskhaving transmissivity equal to the second signal amplitude divided bythe first signal amplitude. In an example of step 640, spot-locationestimator 252 determines location x₂(plot 520, FIG. 5) on optical mask334(2) (FIG. 3) using mask properties 334P.

In step 650, method 600 determines a plurality of candidate locations{x_(3,1), x_(3,2), x_(3,3), . . . , x_(3,n)} in the x-range andcorresponding to locations on the fast-varying optical mask havingtransmissivity equal to the third signal amplitude divided by the firstsignal amplitude. In an example of step 650, spot-location estimator 252determines candidate locations 532 (plot 530, FIG. 5) on optical mask334(3) (FIG. 3).

In step 660, method 600 determines a refined-estimate location, of theplurality of candidate locations, closest to the coarse-estimatelocation x₂. In an example of step 660, spot-location estimator 252determines, from normalized locations 532, normalized location 532(11)as the closest to coarse-estimate location x₂ (plot 520, FIG. 5).

In step 670, method 600 determines, based on the refined-estimatelocation, an angle of the object with respect to a plane perpendicularto the spatial dimension x and intersecting the masks. In an example ofstep 670, position-to-angle-converter 254 determines a measured locationangle 213M, which is a measurement of location angle 313 of object 391with respect to plane 397, which is perpendicular to the x-y plane.

The optical signal introduced in step 610 may be a modulated opticalsignal with a modulation frequency and a corresponding frequency-domainamplitude. In such an instance, method steps 615, 625, and 635 mayimplement steps 710, 720, and 730, shown in FIG. 7. Steps 710, 720, and730 are for example implemented by localization system 200 executingcomputer-readable instructions of software 250, or by a localizationsystem 3300 executing computer-readable instructions of software 2050,as shown in FIG. 33. Herein, indices m₁, m₂, and m₃ each denote adifferent one of channels 231(1−M), that is: m_(1,2,3)∈[1, 2, . . . ,M].Index n₁ denotes an one of emitters 211(1−N), that is: n₁ ∈[1, 2, . . .,N].

In step 710, method 600 demodulates the detected portion to yield abaseband signal. In a first example of step 710, channel 231(m ₁)detects optical signal 212(n ₁) from emitters 211(1−N). Optical signal212(n ₁) is modulated at modulation frequency 212F(n₁), FIG. 2. Channelelectronics 232(m ₁) demodulates optical signal 212(n ₁) to yieldchannel signal 231S(m₁) having a measured modulation frequency amplitude242(n ₁, m₁) corresponding to modulation frequency 212F(n₁). In a secondexample of step 710, channel 231(m ₂) detects signal 212 from emitters211(1−N). Channel electronics 232(m ₂) demodulates optical signal 212(n₁) to yield channel signal 231S(m₂) having a measured modulationfrequency amplitude 242(n ₁, m₂) corresponding to modulation frequency212F(n₁). In a third example of step 710, channel 231(m ₃) detectssignal 212(n ₁) from emitters 211(1−N). Channel electronics 232 (m₃)demodulates optical signal 212(n ₁) to yield channel signal 231S(m₃)having a measured modulation frequency amplitude 242(n ₁, m₃)corresponding to modulation frequency 212F(n₁)

In step 720, method 600 generates a frequency-domain representation ofthe baseband signal. In an example of step 720, frequency domainanalyzer 256 generates a first, second, and third frequency-domainrepresentation of respective channel signals 231S(m₁), 231S(m₂), and231S(m₃).

Step 730 is an optional part of method 600, which localization system200 may implement to find an angular position of an object emitting amodulated optical signal. The angular position is accurate so long asthe baseband signal of step 710 is not corrupted, e.g., by occlusion188.

In step 730, method 600 determines, as the signal amplitude, afrequency-domain amplitude of the frequency-domain representationcorresponding to the modulation frequency. In an example of step 730,frequency domain analyzer 256 determines, as respective first, second,and third signal amplitudes, measured modulation frequency amplitudes242(n ₁, m₁), 242(n ₁, m₂), and 242(n ₁, m₃).

Step 730 may include step 732, in which method 600 determines whetherthe baseband signal is corrupted. Step 730 may also include step 734, inwhich method 600 excises corrupted measurements. FIGS. 8-10 showexemplary corrupted signals and signals processed therefrom, whichillustrate examples of step 732 and 734.

FIG. 8 is a time-series plot 800 of measured voltage corresponding tochannel signals 831S(1) and 831S(2), the latter of which is an exampleof a corrupt baseband signal. Channel signals 831S are both examples ofa channel signal 231S produced by channel electronics 232 oflocalization system 200. Channel signals 831S have a same modulationperiod 812T and corresponding modulation frequency 812F, which is anexample of modulation frequency 212F.

Channel signals 831S(1) and 831S(2) are generated by channels 231(1) and232(2), respectively, of localization system 200 in response to amodulated optical signal 212. Modulated optical signal 212 is, forexample, modulated optical signal 112(2) generated by emitter 111(2),FIG. 1. For sake of clarity, plot 800 displays channel signals 831S asnormalized with DC-bias removed. Hence, plot 800 does not illustrate anydifference in signal amplitudes of channel signals 831S(1,2) caused bytheir respective optical masks 234(1,2) of channels 231(1,2) of FIG. 1.

Plot 800 designates time period 802, during which occlusion 188 of FIG.1 is between emitter 111(2) and receiver 130(2), and channel signal831S(2) deviates from channel signal 831S(1). Deviation of channelsignal 831S(2) from channel signal 831S(1) during time period 802 is anexample of detection of corrupted signal 112C, FIG. 1.

In a first example of step 732, signal evaluator 260 determines thatchannel signal 831S(2) is corrupt by detecting a feature thereof thatdeviates from a predetermined value. For example, during time period802, both the time-averaged value (e.g., over several periods) andamplitude of channel signal 831S(2) differ from the respectivetime-average values and amplitudes in preceding times.

In this example, occlusion 188 is airborne particulate such as dust ordirt. Although corrupted signal 831S(2) of plot 800 results from actualdust/dirt, a corrupted signal similar to corrupted signal 831S(2) mayalso occur in clear-air systems when there are other type of electricalor weather events, extreme motion between the transmitter and codedreceivers, unwanted short-time reflection or jammers as well as failureof a transmitter. Noisy electrical environments such as vehicles or hightransmission power areas may also induce similar changes in clear air.High-voltage transients occur frequently in relay-switched systems suchas diesel or gasoline and electrical powered vehicles, aircraft, boats,and numerous industrial switching systems. Typical fluorescent lightinggenerates both optical and electrical interference and is commonindoors. Incandescent lighting generates the usual 50 Hz and 60 Hznoise. All of these noise sources can potentially corrupt localizationsystem 200 and are mitigated using various processing approaches.

FIG. 9 illustrates a time-series plot 900, which is a frequency-domainanalog of plot 800 showing the effects of airborne dust and dirt onmeasured modulation frequency amplitudes. Time-series plot 900 includesmeasured STFT amplitudes 942(n ₁, m₁) and 942(n ₁, m₂) corresponding todetection of optical signal 212(n ₁) emitted by emitter 211(n ₁) asdetected by respective channels 231(m ₁) and 231(m ₂) of localizationsystem 200. STFT amplitudes 942 are examples of measured signalamplitudes 242. Plot 900 includes a time interval 964 that includes atime t₁ over which STFT amplitudes 942 may be averaged to determine afrequency-domain amplitude at time t₁. Time interval 964 is an exampleof time interval 264.

In this example, optical signal 212(n ₁) has a modulation frequency212F(n₁). Channels 231(m ₁) and 231(m ₂) generate respective channelsignals 231S(m₁) and 231S(m₂). STFT amplitudes 942(n ₁, m₁) and 942(n ₁,m₂) are STFT amplitudes of channel signals 231S(m₁) and 231S(m₂),respectively, corresponding to modulation frequency 212F(n₁) during atime window 910. The STFT has a dwell time (window width) of onemillisecond, during which channel signals 231S(m_(1,2)) were sampledtwo-hundred fifty times, which corresponds to a 250-kHz sample rate.Sample rates may be greater than or less than 250 kHz, up to 1.0 MHz forexample, without departing from the scope hereof.

Time window 910 includes a sub-interval 912 during which airborneparticulates (e.g., dust and/or dirt) between emitter 211(n ₁) and eachchannel 231(m ₁) and 231(m ₂) results in STFT amplitudes 942(n ₁, m₁)and 942(n ₁, m₂) being noisy relative to amplitudes thereof at timesoutside of sub-interval 912. The airborne particulates are examples ofocclusion 188. As shown in plot 900, airborne particulates may eitherreduce or amplify STFT amplitudes 942. Applicant postulates that suchamplification is likely caused by a “lensing” or mirror effect ofparticulates in the presence of direct sun. Similar lensing and mirroreffects are seen with rain drops between one emitter 211 and one channel231.

In optional step 732, method 600 determines whether the baseband signalis corrupted. A second example of step 732 involves exemplary STFTamplitude 942(n ₁,m₁) of emitter 211(n ₁). In this example, signalevaluator 260 determines that the component of channel signal 231S(m₁)corresponding to emitter 211(n ₁) is corrupt because, duringsub-interval 912, its STFT amplitude 942(n ₁,m₁) has a fluctuation 951that exceeds a predetermined range 921. Predetermined range 921 is, forexample, greater than the fluctuation of STFT amplitudes 942 outside ofsub-interval 912.

Occlusion 188 distorts values of measured STFT amplitudes 942, whichresults in inaccurate localization of emitter 211(n ₁). STFT amplitudes942 are examples of frequency-domain amplitudes determined in step 730,optionally used in embodiments of method 600 to determine the first,second, and third signal amplitudes. Method 600 uses the first, second,and third signal amplitudes to determine an object's angularorientation, such location angle 313 of object 391 with respect to plane397, FIG. 3. As such, accurate determination of STFT amplitudes 942 inthe presence of occlusion 188 is essential for localization system 200to accurately locate emitters 211 emitting modulated signals 212.

A third example of step 732 involves prediction errors 1010 and 1020shown in FIGS. 10A and 10B and generated by signal evaluator 260.Prediction errors 1010 and 1020 correspond to STFT amplitudes 942(n ₁,m₁) and 942(n ₁, m₂), respectively. Prediction errors 1010 and 1020result from convolving respective STFT amplitudes 942(n ₁, m₁) and 942(n₁, m₂) with respective linear prediction coefficients. Recall that STFTamplitudes 942(n ₁, m₁) and 942(n ₁, m₂) are STFT amplitudes of channelsignals 231S(m₁) and 231S(m₂), respectively (FIG. 2), corresponding tomodulation frequency 212F(n₁). Outlying values of prediction errors 1010and 1020 are roughly correlated with spikes in respective STFTamplitudes 942(n ₁, m₁) and 942(n ₁, m₂).

Prediction errors 1010 and 1020 correspond to different receive channelsand are essentially uncorrelated. Correlation of prediction errors 1010and 1020 depends on the source of the error. If the error is induced bya transmission-side phenomenon or a system-wide issue that impacts allchannels 231, for example a cloud suddenly blocking the sun, then allthe channels 231 should see a similar error and the prediction errorsbecome correlated. Events occurring closer to the receiver 230 such asdirt or rain drops that only fall in front of one aperture millimetersaway from the sensor cover glass may only affect one channel 231 andresult in uncorrelated prediction errors.

In this example of step 732, signal evaluator 260 determines thatchannel signals 231S(m₁) and 231S(m₂) are corrupt because theirrespective prediction errors exceed a threshold 1021, which equals 0.05in this example as illustrated in both FIGS. 10A and 10B. In anembodiment of localization system 200, signal evaluator 260 calculatesthe linear prediction coefficients in real-time and determines channelsignals 231S(m₁) and 231S(m₂) to be corrupt when respective predictionerrors exceed threshold 1021, FIGS. 10A and 10B. Signal evaluator 260,for example, executes a forward linear predictor using aroot-mean-square criterion or other predictors known in the art.

In optional step 734 of step 730, method 600 excises corruptedmeasurements In an example of step 734, signal conditioner 258 excisesSTFT amplitudes 942 (FIG. 9) that correspond to prediction errors 1010and 1020 exceeding threshold 1021 (FIG. 10).

FIGS. 11A and 11B are plots illustrating the improvement ofsignal-to-noise ratios (SNRs) of STFT amplitudes 942(n ₁, m₁) resultingfrom excision of corrupted data revealed by prediction error 1010 ofFIG. 10A. FIG. 11A shows uncorrected SNR time series 1111 and correctedSNR time series 1112 each computed over non-overlappingfifty-millisecond time intervals (τ_(A)=50 ms) of STFT amplitudes 942(n₁, m₁). FIG. 11B shows uncorrected SNR time series 1121 and correctedSNR time series 1122 each computed over non-overlapping 250-millisecondtime intervals (τ_(B)=250 ms) of STFT amplitudes 942(n ₁, m₁). Timeintervals τ_(A) and τ_(B) are each examples of time interval 964 shownin FIG. 9. SNR monitor 262 may generate time series 1111, 1112, 1121,and 1122.

Time intervals τ_(A) and τ_(B) correspond to respective update ratesR_(A)=1/τ_(A) and R_(B)=1/τ_(B). Hence, the time series of FIG. 11B eachhave a lower update rate compared to those of FIG. 11A.

Uncorrected SNR time series 1111 and 1121 were computed using all valuesof STFT amplitudes 942(n ₁, m₁). Corrected SNR time series 1112 and 1122were computed using only STFT amplitudes 942(n ₁, m₁) with predictionerrors not exceeding threshold 1021. As shown in FIG. 11A, uncorrectedSNR time series 1111 ranges from about zero to a maximum of about onehundred. Corrected SNR time series 1112 ranges from a minimum of about140 to a maximum exceeding one thousand. Absent weather events, i.e.clear air, the uncorrected and corrected SNR time series 1111 and 1112would be approximately constant. Correction of the data yields asignificant increase in SNR, for example, an increased minimum SNR. Theminimum SNR may be used as criterion for performance of localizationsystem 200. For example, FIG. 11A denotes a minimum SNR 1130 as SNR₁₁₃₀,which equals two hundred, for example.

In FIG. 11B, uncorrected SNR time series 1121 ranges from about zero toa maximum of about one hundred. An occlusion event is clearly seenbetween four seconds and nineteen seconds, where uncorrected SNR timeseries 1121 decreases by nearly an order of magnitude. Corrected SNRtime series 1122 ranges from a minimum of about four hundred to amaximum exceeding five thousand. Increasing the time interval 264increases the minimum SNR of the corrected data by approximately thesquare root of the time-increase factor. The time-increase factor forSNR time series 1112 and 1122 is five, such that the ratio of respectiveminima of SNR time series 1112 to SNR time series 1111 should beapproximately √{square root over (5)}≈2.2. The minimum of corrected SNRtime series 1122 (≈400) is approximately 2.9 times that of the minimumof corrected SNR time series 1112 (≈140).

Step 730 may include steps 736 and 738. In step 736, method 600determines, as the signal amplitude, an average of a short-time Fouriertransform amplitude within a time interval. In an example of step 736,frequency domain analyzer 256 determines an average of STFT amplitudes942(n ₁, m₁) within time interval 964.

In optional step 738, method 600 adjusts the time interval according toa signal-to-noise ratio of the determined STFT short-time Fouriertransform amplitude. In an example of step 738, the time interval ofstep 736 is τ_(A) of FIG. 11A. In this example of step 738, SNR monitor262 increases time interval 264 from τ_(A) to τ_(B) because the minimumof SNR time series 1112 is below a predetermined threshold, such as SNR1130.

Method 600 may repeat step 736 after step 738 to yield a signalamplitude with an increased signal to noise ratio. The increased timeinterval results in the signal amplitude, that is, average of STFTamplitudes 942(n ₁, m₁) within time interval 964, having a higher SNR,as shown by comparing SNR time series 1122 to SNR time series 1112.Increasing time interval 964, an example of time interval 264, maintainsaccuracy of measured locations angles 213M generated by localizationsystem 200, while decreasing the update rate thereof.

FIG. 12 is a plot 1201 of a corrupted baseband signal 1231S(m) generatedby channel 231(m) in response to emitters 211 emitting respectivemodulated optical signals 212 with associated modulation frequencies212F. Signal 1231S(m) is similar to channel signal 831S(2) by virtue oftheir both including noise. Corruption of baseband signal 1231S issimilar to the corruption of channel signal 831S(2) in FIG. 8.Modulation frequencies 212F include a modulation frequency 212F(n₁)corresponding to emitter 211(n ₁). Corrupted baseband signal 1231S(n)spans a time duration 1212 and is an example of a channel signal 231S,such as channel signal 831S(2) that is also corrupted by noise. Basebandsignal 1231S includes noise components 1204 that each contributefrequency domain amplitudes to a frequency-domain representation ofcorrupted baseband signal 1231S. Corrupted baseband signal 1231S has ameasured frequency-domain corresponding to modulation frequency212F(n₁). The time variation of this frequency-domain amplitude issimilar to those of STFT amplitudes 942 during sub-interval 912, FIG. 9.

Time duration 1212 includes a plurality of intervals 1264(1, 2, . . .Q), which may be overlapping. Intervals 1264 are examples of timeinterval 264 of localization system 200, shown in FIG. 2. The timeduration of each interval 1264 exceeds a maximum modulation periodT_(1231S) of baseband signal 1231S corresponding to the inverse of thesmallest of modulation frequencies 212F. For example, each interval 1264has a duration 250·T_(1231S). FIG. 13 illustrates a plurality of STFTamplitude estimates 1342E(1, 2, . . . , Q), which correspond to arespective interval 1264(1, 2, . . . , Q). STFT amplitude estimates1342E corresponds to modulation frequency 212F(n₁). STFT amplitudeestimates 1342E have a minimum value A₁ and a maximum value A₂₀, whichare illustrated in FIG. 14.

FIG. 14 depicts histograms 1410 and 1420 illustrating occurrences ofSTFT amplitude estimates 1342E. The total number of occurrences in eachhistogram is Q. Histograms 1410 and 1420 have horizontal axes that spanSTFT amplitudes A₁-A₂₀. Histogram 1410 has bins 1412 that each spanadjacent odd-indexed STFT amplitudes. Histogram 1420 has bins 1422 thateach span adjacent even-indexed STFT amplitudes. Bins 1422 and 1412 areshifted with respect to one another by one-half a bin width. Within bins1412 of histogram 1410, the bin with the highest number of occurrencesis centered on STFT amplitude A₈, as indicated by count 1428. Withinbins 1412 and 1422 of histograms 1410 and 1420, the bin with the highestnumber of occurrences is centered on STFT amplitude A₉, as indicated bycount 1429. Hence, STFT amplitude A₉ may be considered a most likelyamplitude of modulation frequency 212F(n₁). STFT amplitude A₉ is anexample of either a first, second, or third signal amplitude determinedby step 615, step 625, or step 635 respectively, of method 600 FIG. 6.

FIG. 15 is a flowchart illustrating a method 1500 for determining alocalization parameter of an object. Method 1500 is, for example,implemented by localization system 200 executing computer-readableinstructions of software 250, or by localization system 3300 executingcomputer-readable instructions of software 2050, as shown in FIG. 33.Step 730 (FIG. 7) may employ method 1500 to determine the signalamplitude. FIGS. 12-15 are best viewed together in the followingdescription.

Method 1500 includes step 1520, step 1530, step 1540, and an optionalstep 1510. In step 1510, method 1500 conditions the baseband signal byapplying a discrete difference operator thereto. Step 1510 yields aconditioned baseband signal. In an example of step 1510, signalconditioner 258 applies a discrete difference operator to basebandsignal 1231S, which results in a conditioned baseband signal. Examplesof a discrete difference operator are the “numpy.diff” function, of theSciPy open-source library for the Python programming language, and the“diff” function in MATLAB®.

In step 1520, method 1500 generates a plurality of estimates of a firstfrequency-domain amplitude of a baseband signal from the object. Each ofthe plurality of estimates corresponds to a respective one of aplurality of temporal segments of the baseband signal. The firstfrequency-domain amplitude corresponds to a temporal frequency of thebaseband signal. When method 1500 does not include step 1510, thereceived baseband signal is the baseband signal. When method 1500includes step 1510, a baseband signal is the conditioned basebandsignal. In a first example of step 1520, frequency domain analyzer 256generates STFT amplitude estimates 1342E(1, 2, . . . , Q) fromrespective intervals 1264(1, 2, . . . , Q) of baseband signal 1231S. Ina second example of step 1522, frequency domain analyzer 256 generatesSTFT amplitude estimates 1342E(1, 2, . . . , Q) from respectiveintervals 1264(1, 2, . . . , Q) of baseband signal 1231S conditioned bysignal conditioner 258.

In step 1530, method 1500 determines the frequency-domain amplitude asmost common value of the estimates. In an example of step 1530,frequency domain analyzer 256 determines frequency-domain amplitude A₉as the most common value of STFT amplitude estimates 1342E.

Step 1530 may include steps 1522 and 1524. In step 1522, method 1500bins the plurality of estimates into a plurality of bins, each bincorresponding to a respective interval between a maximum of theplurality of estimates and a minimum of the plurality of estimates. Instep 1524, method 1500 determines the frequency-domain amplitude as anestimate within the bin corresponding to the interval having thegreatest number of estimates.

In a first example of steps 1522 and 1524, frequency domain analyzer 256generates histogram 1410 and determines frequency-domain amplitude A₈ asthe most common value of STFT amplitude estimates 1342E. In a secondexample of steps 1522 and 1524, frequency domain analyzer 256 generateshistograms 1410 and 1420 determines frequency-domain amplitude A₉ as themost common value of STFT amplitude estimates 1342E.

In step 1540, method 1500 determines the localization parameter based onthe first frequency-domain amplitude. In an example of step 1540,position-to-angle-converter 254 of localization system 200 determines ameasured location angle 213M.

FIG. 16A is a plot comparing raw STFT amplitude estimates 1612 (solidlines) and refined STFT amplitude estimates 1614 (dotted line). Raw STFTamplitude estimates 1612 are examples of STFT amplitude estimates 1342Eand have a signal-to-noise ratio of 41.3. Refined STFT amplitudeestimates 1614 are examples of frequency-domain amplitude A₉ (FIG. 12)as generated by system 200 implementing method 1500 without step 1510.STFT amplitude estimates 1614 have a signal-to-noise ratio of 989.7.

FIG. 16B is a plot comparing raw STFT amplitude estimates 1622 (solidlines) and refined STFT amplitude estimates 1624 (dotted line). Raw STFTamplitude estimates 1622 are examples of STFT amplitude estimates 1342Eand have a signal-to-noise ratio of 41.2. Refined STFT amplitudeestimates 1624 are examples of frequency-domain amplitude A₉ (FIG. 12)as generated by system 200 implementing method 1500 with step 1510. STFTamplitude estimates 1624 have a signal-to-noise ratio of 1140.1, whichis fifteen percent higher than the signal-to-noise ratio of STFTamplitude estimates 1614.

FIG. 17 is a time-series plot of measured STFT amplitudes 1742(n ₁,m₁)and 1742(n ₁, m₂) corresponding to detection of optical signal 212(n ₁)emitted by emitter 211(n ₁) as detected by respective channels 231(m ₁)and 231(m ₂) of localization system 200. STFT amplitudes 1742 areexamples of measured signal amplitudes 242 and are similar to STFTamplitudes 942 of FIG. 9.

FIG. 18 shows histograms 1810 and 1820 generated from STFT amplitudes1742(n ₁, m₁) and 1742(n ₁, m₂), respectively. Histograms 1810 and 1820are examples of histogram 1410, FIG. 14, and result from step 1530 ofmethod 1500. Histograms 1810 and 1820 have respective most-common values1811 and 1821, which are both examples of the most common value offrequency-domain amplitude estimates determines in step 1530.

FIGS. 19A and 19B are plots of prediction errors 1910 and 1920 of STFTamplitudes 1742(n ₁, m₁) and 1742(n ₁, m₂), respectively. Predictionerrors 1910 and 1920 are similar to prediction errors 1010 and 1020shown in FIG. 10. Prediction errors 1910 and 1920 that exceed athreshold 1902 correspond to a corrupt STFT amplitude 1742. In thefollowing discussion, threshold 1902 equals 3.1×10⁻⁵. Corrupt amplitudesof STFT amplitudes 1742 are those that yield a prediction error 1910,1920 that exceeds threshold 1902.

In an embodiment of method 600, step 732 evaluates an STFT amplitudecorresponding to a baseband signal to determine if the baseband signalis corrupt. In an example of step 732, signal evaluator 260 determinesthat a baseband signal (e.g., a channel signal 231S) corresponding to anSTFT amplitude 1742 is corrupted when its prediction error 1910 or 1920exceeds threshold 1902.

FIG. 20 is a plot of STFT ratio 2010, which is the ratio of STFTamplitude 1742(n ₁, m₁) to STFT amplitude 1742(n ₁, m₂). Ideally, STFTamplitudes 1742(n ₁, m₁) and 1742(n ₁, m₂) would have respective meanvalues with a small amount of statistical noise. Due to the weatherevents, snow in this case, the STFT amplitudes 1742(n ₁,m₁) and 1742(n₁, m₂) have large variations, which STFT amplitude ratio 2010illustrates. Estimates of a time-average value of STFT amplitude ratio2010 will either have a large bias, variance or both, which means thatSTFT amplitude ratio 2010 is badly corrupted.

FIG. 21 is a plot of corrected STFT ratio 2110, which is the ratio ofSTFT amplitude 1742(n ₁, m₁) to STFT amplitude 1742(n ₁, m₂) withcorrupt amplitudes removed. These corrupt amplitudes are shown in FIGS.19A, B. Compared to STFT amplitude ratio 2010, corrected STFT amplituderatio 2110 has a constant value with little variation due to noise. TheSNR of STFT amplitude ratio 2010 approaches that of ideal data for astationary system with no relative motion.

In an embodiment of method 600, step 732 evaluates a STFT amplituderatio corresponding to a baseband signal to determine if the basebandsignal is corrupt. In an example of step 732, signal evaluator 260determines that a baseband signal (e.g., a channel signal 231S)corresponding to an STFT amplitude 1742 is corrupted when STFT amplituderatio 2010 has a variance that exceeds a predetermined value.

FIG. 22 is a plot of SNR time series 2210 and SNR time series 2220corresponding to STFT ratios 2010 and 2110, respectively. SNR timeseries 2210 and 2220 were computed with non-overlapping time intervals264 having a 25-ms duration, in which each interval includes twenty-sixshort-time Fourier transform samples with a duration of 0.952milliseconds. SNR time series 2210 ranges from a minimum of about zeroto a maximum of about one thousand. SNR time series 2220 ranges from aminimum of about one thousand to a maximum of over 3000. Absent weatherevents, i.e. with clear air, SNR time series 2210 and 2220 would beapproximately constant. Correction of the data yields a significantincrease in SNR and minimum SNR. Minimum SNR is may be a criterion forsystem performance.

FIG. 23 illustrates an optical component array 2300 present in anembodiment of receiver 230 of localization system 200 of FIG. 2. Array2300 includes a lens mount 2310 holding lenses 2311, a spacer 2320having windows 2321, a lens mount 2330 holding lenses 2331, a spacer2340 having windows 2341, and an optical mask assembly 2350 thatincludes optical masks 2351(1, 2, . . . , N). While N equals sixteen inarray 2300, it may equal to different positive integer without departingfrom the scope hereof. Each optical mask 2351 may be mutually distinct.Alternatively, two or more optical masks 2351(1, 2, . . . , N) may beidentical. One or more optical mask 2351 may be a clear mask, anaperture through optical mask assembly 2350, for example.

Each optical mask 2351 is an example of optical mask 234 of channel 231and is aligned with a respective lens 2311 of lens mount 2310, window2321 of spacer 2320, lens 2331 of lens mount 2330, and window 2341 ofspacer 2340. For example, optical mask 2351(1) is aligned with window2341(1), lens 2331(1), window 2321(1), and lens 2311(1). Windows 2321and 2341 may be apertures through respective spacers 2320 and 2340.

Mount 2310, spacer 2320, mount 2330, spacer 2340, and assembly 2350 areseparated by distances 2361, 2362, 2363, and 2364 as shown in FIG. 23.Distance 2361-2364 and respective focal lengths of lenses 2311 and 2331may be configured such that optical signals 212 propagating through alens 2311 and 2331 and windows 2321 and 2341 aligned with an opticalmask 2351 are either (a) focused thereon or (b) focused to a planeparallel and proximate to mask 2351 such that aforementioned defocusdistance Δ is non-zero, e.g., when mask 2351 is binary and periodic.Distances 2361 and 2362 may both equal zero such that thickness ofspacer 2320 defines a distance between lens mounts 2310 and 2330.Distances 2363 and 2364 may both equal zero such that thickness ofspacer 2340 defines a distance between lens mount 2330 and optical maskassembly 2350.

Spacers 2320 and 2340 may be opaque to carrier frequency 212C, e.g., toat least one of visible and near-IR light, and function to prevent straylight from reaching an optical mask 2351. For example, windows 2321(1)and 2341(1) may be configured, e.g., sized, to prevent light propagatingthrough lenses 2311(1) or 2331(1) from reaching optical mask 2351(2).

When each distance 2361-2364 equals zero, optical component array 2300may be monolithic such that it is constructed with a single type ofoptical material in order to reduce the system effects of temperature.Optical components typically change size and form as a function oftemperature. Construction of optical component array 2300 with thermallysimilar or identical materials results in all planes of opticalcomponent array 2300 moving similarly, which enables an effective methodto control the system effects of temperature. Hence, while all planessimilarly change as a function of temperature, each plane is undergoingessentially the same changes, which makes the relative changes betweenplanes unnoticeable when measuring light on the detectors after the maskassembly.

FIG. 24 is a schematic diagram of a static transmitter-receiver pair2400. Transmitter-receiver pair 2400 includes a transmitter 2411, whichis an example of emitter 211 of FIG. 2, and receiver 230 shown in FIG.2. Transmitter 2411 includes light source 215. Transmitter 2411 andreceiver 230 are separated by distance R.

FIG. 25 is a schematic diagram of a static transmitter-receiver pair2500. Transmitter-receiver pair 2500 includes a transmitter 2511,receiver 230, and a light source 2522. Transmitter 2511 includes aretroreflector 2511R configured to direct light emitted by light source2522 toward receiver 230. Retroreflector 2511R may include one or moreof a mirror, a retroreflector, a light engine, a light pipe, are-imager, and a projector. Light source 2522 and receiver 230 areseparated by distance R.

FIG. 26 is a schematic diagram of a localization system 2600 thatincludes receiver 230 and optical transmitter 2620. Optical transmitter2620 illuminates regions of an object 2611. Object 2611 is an example ofemitter 211. Optical transmitter 2620 is an example of opticaltransmitter 220, and includes a mirror 2632 that reflects light 2633Lemitted by a light source 2633 toward object 2611 located a distance Rtherefrom. Light source 2633 is an LED or laser diode, for exampleMirror 2632 may include at least one of a rotating-scanning mirror and amicro-electro-mechanical systems (MEMs) mirror. Object 2611 has a topend 2611T and a bottom end 2611B, respectively, and a front surface2611F therebetween. Front surface 2611F may include a barcode or otheroptical, machine-readable, representation of data.

Mirror 2632 may direct light 2633L toward object 2611 to an illuminatedlocation 2621 such that optical transmitter 2620 scans front surface2611F along a path 2624 thereon. Path 2624 may traverse top end 2611T tobottom end 2611B or vice versa. Motion of illuminated location 2621enables localization over a large region of points on surface 2611F bymoving the mirror 2632 as a function of time, for example, by atime-varying mirror rotation angle θ₂₆(t). Depending on the movement ofthe light 2633L, and hence illuminated location 2621, localization intwo or more dimensions is possible. Illuminated location 2621 may alsobe dynamically controlled to interrogate different regions of the object2611.

Object 2611 reflects light 2633L incident thereon as optical signal2612, which is an example of optical signal 212. At any point in time, aportion of optical signal 2612 is directed toward receiver 230 such thatprocessing unit 280 determines the estimated location of the illuminatedregion on the object. Coordination between the scanning mirror 2632 andreceiver 230 is not required. Light 2633L need not form any particularpattern, such as a grid, on front surface 2611F. A random pattern maysuffice depending on the temporal needs of the overall system.

FIG. 27 is a schematic diagram of a transmitter-receiver pair 2700 thatincludes a rotating emitter 2711 and receiver 230 separated by distanceR. Emitter 2711 is an example of emitter 211. Rotating emitter 2711includes one fixed light source 215 configured to emit beam 2712 at arotation angle θ₂₇ with respect to a front surface of receiver 230.Rotation angle θ₂₇ may vary in time as θ₂₇(t). Rotating emitter 2711 maybe a rotary laser level. Rotating emitter 2711 may include a MEMs mirrorconfiguration such for changing angle θ₂₇. Beam 2712 is an example ofoptical signal 212, and may be a structured beam such as a line or fanor multiple lines or circular beams, periodic or otherwise, or otherspatially structured signal.

Source/receiver pairs 2400, 2500, and localization system 2600experience a R⁻² drop in detected signal power at the receiver as afunction of distance R. Since the size of beam 2712 on receiver 230increases linearly in each transverse dimension as a function ofdistance R, total optical power detected over a constant area decreasesas R⁻². In transmitter-receiver pair 2700, sweeping beam 2712 through atleast one complete beam width enables receiver 230 to capture of allthis radiated optical power in a rotation plane of rotation angle θ₂₇.Localization system 200 processes output of receiver 230 to angularlylocalize rotating emitter 2711 in a plane perpendicular to the rotationplane. Hence, in transmitter-receiver pair 2700, the optical powerdetected by receiver 230 decreases by a factor of R⁻¹(not R⁻²) as afunction of R. The result is that transmitter-receiver pair 2700, canhave a far larger range for a given received amount of power, or SNR,compared a fixed-beam system.

Receiver 230 of localization system 2600 and transmitter-receiver pair2700 may include optical component array 2300 of FIG. 23. Optical signal2612 (FIG. 26) and beam 2712 (FIG. 27) may work in conjunction withoptical component array 2300 to provide a spatiotemporal or time-spacedimension for the processing system to determine additional operationalparameters, as shown in FIG. 28.

FIG. 28 illustrates a temporal wavefront 2805 traversing a receiver 2800in a direction 2806. Temporal wavefront 2805 is, for example, awavefront of optical signal 2612 or 2712 and traverses receiver 2800according to temporal dependence of angles θ₂₆(t) or θ₂₇(t). Temporalwavefront 2805 that has a finite width 2810 of detectable energy acrossa receiver 2800.

Receiver 2800 is an example of receiver 230 of FIG. 2 and includes aplurality of channels 2831 arranged in a two-dimensional array.Accordingly, receiver 2800 may include an embodiment of opticalcomponent array 2300, shown in FIG. 23. Each channel 2831 is in one of aplurality of channel columns 2841-2844. Channels 2831 include aplurality of non-periodically-spaced channels, denoted within a dashedbox 2831B in FIG. 28. In this example, receiver 2800 has non-periodicspacing of channels 2831 to facilitate a spatial separation from theother, periodically-spaced, channels for a constant angular velocity ofsweep rate.

As temporal wavefront 2805 traverses receiver 2800, not all channels2831 initially detect wavefront 2805. Depending on channel spacing andwidth 2810 of wavefront 2805, more than channel column 2841-2844simultaneously detect wavefront 2805, albeit with different energies asa function of time, as shown in FIGS. 29-32. In FIG. 29, channels ofchannel column 2841 detect wavefront 2805. In FIG. 30, channels 2831 inchannel column 2842 and 2843 detect wavefront 2805. In FIG. 31, channels2831 of channel column 2842 and 2843 detect wavefront 2805. In FIG. 32,channels 2831 of channel column 2843 and 2844 detect wavefront 2805.

Relative angular orientation between receiver 2800 and an emitter suchas 2611 or 2711 may be estimated via a temporal signatures of the timeof arrival of wavefront 2805 across channels 2831, as shown in FIG. 32.Whereas all channels 2831 in columns 2842 and 2843 detect wavefront 2805in FIG. 30, two of the four channels of column 2844 detect wavefront2805 in FIG. 32, where receiver 2800 is rotated relative to itsorientation of in FIG. 30. Such incomplete illumination of channels 2831in a channel column 2844 indicates a tilt of receiver 2800 with respectto a propagation of direction of an optical signal 212, such as opticalsignal 2612 and beam 2712. Uniqueness in the temporal signature can beused to determine beam width, or distance from the transmitter for abroadening source.

FIG. 33 illustrates one exemplary localization system 3300, which is anexample of processing unit 280 of localization system 200. Localizationsystem 3300 is configured to determine a frequency-domain amplitude 3342of a baseband signal 3331 having a temporal frequency component. Thefrequency-domain amplitude corresponds to the temporal frequencycomponent. Baseband signal 3331 and frequency-domain amplitude 3342 areexamples of channel signal 231S and measured signal amplitude 242,respectively of localization system 200.

Localization system 3300 includes microprocessor 282 and a memory 3484,which is an example of memory 284. Memory 3484 stores software 2050 andoptionally time interval 264. Software 2050 includes frequency domainanalyzer 256 and optionally spot-location estimator 252,position-to-angle converter 254, signal conditioner 258, signalevaluator 260 and SNR monitor 262. Software 250 of FIG. 2 is an exampleof software 2050.

Localization system 3300 may also be configured to determine alocalization parameter 3313 from frequency-domain amplitude 3342.Localization parameter 3313 is, for example, a measured location angle213M shown in FIG. 2. Localization parameter 3313 may be a distancebetween the object and a receiver that detects an electromagnetic signalpropagating from the object, e.g., when localization system 3300 is usedfor ranging.

FIGS. 34-38 describe exemplary uses of localization system 200 andmethod 600. Each transmitter 3411 of FIGS. 34-38 is an example of anemitter 211. Vehicle 184 of FIG. 34 has a transmitter 3411(1) above itsdriver's seat and a transmitter 3411(2) on pallet 3484, which enablesboth location and state of the lift (and pallet 3484) to be estimated,displayed and potentially controlled. Bicycle 3520 of FIG. 35 has atransmitter 3411(3) enables it to be localized and potentiallycontrolled.

Mobile rack 3630 of FIG. 36 may include a range of trackable objects,such as object 3632 via transmitter 3411(4). The location of specificregions of rack 3630 may be estimated by localizing transmitters 3411(5)and 3411(6). Transmitter 3411(5) may serve an additional role by virtueof its being on the bottom shelf of rack 3630. When the rack 3630 isempty, transmitter 3411(5) becomes visible to localization system 200,enabling not only a location estimate but the knowledge that rack 3630is empty. Mobile stair 3740 of FIG. 37 is similarly trackable viatransmitter 3411(7).

In an exemplary use case of localization system 200 that includes atransmitter 3411, transmitter 3411 may be placed in locations that arenot normally visible, such as the sole of footwear or hidden beneathhigh value items that should not be moved, or indicate potential issuesin the environment. Transmitters 3411 visible from soles of shoes mayindicate a person in a prone position, possibly from an accident. Atransmitter 3411 may also indicate a missing item when an obstructed andtransmitter 3411 is suddenly revealed when the obstruction is removed,enabling real-time theft detection or notification of abrupt changes inan otherwise static environment.

Vest 3850 of FIG. 38 is a specialized vest wearable by workers, visitorsand operators at a facility or job site. Vest 3850 is specialized inthat it has transmitting regions 3851, 3852 either on or within thematerial of the vest. Transmitting regions 3851 and 3852 are examples ofemitters 211. These vests may incorporate wearable electronics to makethe transmitter systems less bulky, more acceptable to wearers andpotentially less cost and more technically effective as transmitters.Transmitting region 3851 may transmit light generally upward foridentification and localization. Transmitting region 3852 may transmitlight generally horizontally when worn in the traditional manner, butalso vertically when the wearer is sitting, lying down, etc. A wearer ofvest 3850 may also carry additional temporary transmitters 3853 to beplaced on items of interest for tracking in a temporary fashion, forexample to track the passage of a high value item from shelf toshipping. In such a case, one temporary transmitter 3853 would beactivated by the user and logged into the infrastructure by thereceivers to begin tracking. A selected temporary transmitter 3853 canbe removed from the high-value item prior to shipping and recirculatedinto a pool of temporary transmitters 3853.

FIG. 39 illustrates an exemplary use environment 3980 for a localizationsystem 3900 communicatively coupled to controller 260. Localizationsystem 3900 is an example of localization system 200. Environment 3980includes fixed landmarks 3982(1-N), which are similar to fixed shelves182 of FIG. 1. Each landmark 3982 has one or more Mutually distincttransmitters 3911 configured to emit a distinct optical signal 3912.Transmitters 3911 and optical signal 3912 are examples of emitters 211and optical signal 212 respectively.

Quantity N may range from less than ten to greater than a thousand.Landmarks 3982 have respective lengths 3982L(1-N), each of which may beless than ten meters long to thousands of meters long. While FIG. 39illustrates landmarks 3982 as being mutually parallel, landmarks 3982may have other relative orientations. For example, their relativeorientation can be simple as a grid or a complex as the streets of amedieval city.

Transmitters 3911 function to identify regions and locations of thefixed landmarks 3982. A landmark 3982 may have any number oftransmitters 3911, for example, ranging from less than ten to more thanone thousand, depending on the application.

Application environment 3980 includes a mobile object 3984 beingdirected to a location 3988 along a path 3986 by localization system3900 and controller 260. Object 3984 has thereon a transceiver 3985,which is an example of an emitter 211 that includes receiver 217.Transceiver 3985 is for example communicatively coupled to object 3984such that controller 260 may remotely operate object 3984 viatransceiver 3985. Controller 260 executes processing and control tocalculate a desired path 3986 and command mobile object 3984 travel path3986, via instructions 3964. Communication to object 3984 can beperformed optically or wirelessly through transceiver 3985. Localizationsystem 3900 estimates position, velocity and other relevant informationabout object 3984, such as potential obstructions while object 3984travels path 3986. When object 3984 arrives at location 3988, controller260 may instruct object 3984, via localization system 3900, to perform aspecialized task, such as picking up parts, depositing parts to a fixedlandmark 3982, or reading a barcode.

FIG. 40 depicts a system 4080 that may be used in conjunction withmobile object 3984 of FIG. 39. System 4080 can also be mounted on afixed system. System 4080 includes a substrate 4003 that has a roboticarm 4010 and a localization system 4000 mounted thereon. Localizationsystem 4000 is an example of localization system 200 and includeslocalization receivers 4030(1) and 4030(2). Localization receivers4030(1) and 4030(2) are each examples of receiver 230.

Robotic arm 4010 includes a plurality of actuators 4012(1-3). Typically,multiple actuators are used to control mechanical motion and result inwhat is called open-loop control. Open-loop control does not allow thesystem to automatically compensate for permanent or temporary errors inthe expected position of one or more actuators. Open-loop control alsomeans that picking and placing objects in a fashion as efficient as ahuman is often difficult to impossible, especially if the robot needs tobe relatively low cost. A human's vision coordinated to her hand is aform of closed-loop control. System 4080 in essence enables closed-loopcontrol of a low-cost robot that can mimic the method humans employ touse arms and hands.

Robotic arm 4010 contains an arm 4020 with one or more actuatable parts4021. Actuatable parts 4021 for example resemble fingers of a humanhand. Alternatively, actuatable part 4021 may be a bucket attached toheavy machinery such as an excavator or a crane; for example, arm 4020is a boom and actuatable part 4021 is hydraulic cylinder actuated byactuator 4012(1).

Mounted on actuatable parts 4021 are mutually distinct transmitters 4011that enable precision and fast localization of each actuatable part 4021through localization receivers 4030(1) and 4030(2). Localization ofactuatable parts 4021 can be made relative to one or more referencepoints 4014. Reference points 4014 are for example transmitters 4011 andtransmitters 711 of FIG. 7.

Transmitted radiation 403 land 4032 from actuatable parts 4021 andtransmitted radiation 4033 from reference point 4014 travel towardlocalization receivers 4030(1) and 4030(2). Receivers 4030(1) and4030(2) deliver localization information of each actuatable part 4021and reference point 4014 to processing unit 280 via localization data4009(1) and 4009(2), from which processing unit 280 determineslocalization angles 4013M, which are examples of localization angles213M. Localization data 4009(1) and 4009(2) are examples of localizationdata 209.

Other systems that require actuatable parts 4021 to be in certainpositions or have certain motion, for example to pick up a complex part,Such positions and motion may be inputs for system 4080, and may berepresented by commanded locations 4082. Processing unit 280 comparescommanded locations 4082 to a location determined from measuredlocalization angles 4013M to determine an error signal and updatedlocation commands 4061, which are received by motion actuator 4060. Bycomparing commanded location with actual location, true closed-loopcontrol of actuatable parts 4021 is possible. Position encoders on themotion actuators within robotic arm 4010 are not required. In fact, withclosed-loop control motion actuators can be inexpensive and/or havemotion paths unusual compared to classical robots that moverectilinearly. Motion of the arm 4020 and actuatable parts 4021 mayresemble a human arm and fingers respectively. Closed-loop control wouldenable fast and reliable action similar to how a human's sight and braincontrols the human's hands and fingers. Picking and placing complexobjects is not only possible but relatively simple and low cost withangular coding for closed-loop control.

Combinations of Features

Features described above as well as those claimed below may be combinedin various ways without departing from the scope hereof. The followingexamples illustrate some possible, non-limiting combinations:

(A1) denotes method for determining a localization parameter of anobject. The method includes generating a plurality of estimates of afirst frequency-domain amplitude of a baseband signal from the object.Each of the plurality of estimates corresponds to a respective one of aplurality of temporal segments of the baseband signal. The firstfrequency-domain amplitude corresponds to a temporal frequency of thebaseband signal. The method also includes determining the firstfrequency-domain amplitude as most common value of the plurality ofestimates and determining the localization parameter based on the firstfrequency-domain amplitude.

(A2) In the method denoted by (A1), the step of determining the firstfrequency-domain amplitude may include (i) binning the plurality ofestimates into a plurality of bins, each of the plurality of binscorresponding to a respective interval between a maximum of theplurality of estimates and a minimum of the plurality of estimates, and(ii) determining the first frequency-domain amplitude as an estimatewithin one of the bins that corresponds to the interval having thegreatest number of estimates.

(A3) In the method denoted by (A2), the plurality of bins may include(i) a first plurality of bins corresponding to a first plurality ofintervals each with a respective center and a respective edge, and (ii)a second plurality of bins corresponding to a second plurality ofintervals shifted with respect to the first plurality of intervals suchthat a center of each of the second plurality of intervals correspondsto an edge of one of the first plurality of intervals.

(A4) Any method denoted by (A2), may further include, before the step ofgenerating a plurality of estimates, pre-processing the baseband signalusing a temporal differencing algorithm.

(A5) Any method denoted by one of (A1) through (A4) my further include(i) detecting a first portion of an optical signal from the object, theoptical signal being modulated at the temporal frequency, (ii) detectinga second portion of the optical signal transmitted through aslow-varying optical mask having a strictly monotonic transmissivityT₂(x), in an x-range of a spatial dimension x, (iii) detecting a thirdportion of the optical signal transmitted through a fast-varying opticalmask having a spatially-varying transmissivity T₃(x) having a same valueat more than one value of x in the x-range, and (iv) demodulating one ofthe detected first portion, the detected second portion, and thedetected third portion to yield the baseband signal.

(A6) Any method denoted by (A5), in which the one of the detected firstportion, the detected second portion, and the detected third portion isthe detected first portion, may further include (i) demodulating thedetected second portion to yield a second baseband signal, (ii)generating a second plurality of estimates, of a second frequency-domainamplitude corresponding to the temporal frequency, each corresponding toa respective one of a plurality of second temporal segments of thesecond baseband signal, (iii) determining the second frequency-domainamplitude as most common value of the second plurality of estimates,(iv) demodulating the detected third portion to yield a third basebandsignal, (v) generating a third plurality of estimates, of a thirdfrequency-domain amplitude, corresponding to the temporal frequency,each corresponding to a respective one of a plurality of third temporalsegments of the third baseband signal, and (vi) determining the thirdfrequency-domain amplitude as most common value of the third pluralityof estimates.

(A7) Any method denoted by (A6) may further include (i) determining acoarse-estimate location x₂ in the x-range and corresponding to alocation on the slow-varying optical mask having transmissivity equal tothe second frequency-domain amplitude divided by the firstfrequency-domain amplitude, (ii) determining a plurality of candidatelocations {x_(3,1), x_(3,2), x_(3,3), x_(3,n)} in the x-range andcorresponding to locations on the fast-varying optical mask havingtransmissivity equal to the third frequency-domain amplitude divided bythe first frequency-domain amplitude, (iii) determining arefined-estimate location, of the plurality of candidate locations,closest to coarse-estimate location x₂, and (iv) determining thelocalization parameter, based on the refined-estimate location, as anangle of the object with respect to a plane perpendicular to the spatialdimension x and intersecting the slow-varying optical mask and thefast-varying optical mask.

(B1) A localization system includes a memory and a microprocessor. Thememory stores non-transitory computer-readable instructions and isconfigured to store a baseband signal having a temporal frequencycomponent and a corresponding first frequency-domain amplitude. Themicroprocessor is adapted to execute the instructions to: (i) generate aplurality of estimates of the first frequency-domain amplitude, whereineach of the plurality of estimates corresponds to a respective one of aplurality of temporal segments of the baseband signal, and (ii)determine the first frequency-domain amplitude as most common value ofthe plurality of estimates.

(B2) In the localization system denoted by (B1) the microprocessor maybe further adapted to execute the instructions, when determining thefirst frequency-domain amplitude, to: (i) bin the plurality of estimatesinto a plurality of bins, each of the plurality of bins corresponding toa respective interval between a maximum of the plurality of estimatesand a minimum of the plurality of estimates, and (ii) determine thefirst frequency-domain amplitude as an estimate within the bincorresponding to the interval having the greatest number of estimates.

(B3) In the localization system denoted by (B2), the plurality of binsmay include (i) a first plurality of bins corresponding to a firstplurality of intervals each with a respective center and a respectiveedge, (ii) a second plurality of bins corresponding to a secondplurality of intervals shifted with respect to the first plurality ofintervals such that a center of each of the second plurality ofintervals corresponds to an edge of one of the first plurality ofintervals.

(B4) In any localization system denoted by one of (B2) and (B3), themicroprocessor may be further adapted to execute the instructions to,before the step of generating a plurality of estimates: pre-process thebaseband signal using a temporal differencing algorithm.

(B5) Any localization system denoted by one of (B1) through (B4) mayfurther include: (i) a receiver including a first channel, a secondchannel, and a third channel. The first channel includes (i) a firstlens for receiving a first portion of an optical signal from the object,and (ii) a first photodetector for converting the received firstportion, into a first electrical signal having the firstfrequency-domain amplitude, the optical signal being modulated at thetemporal frequency. The second channel includes (i) a second lens fordirecting a second portion of the optical signal toward a slow-varyingoptical mask having a strictly monotonic transmissivity T₂(x) in anx-range of a spatial dimension x, and (ii) a second photodetector forconverting the second portion, transmitted through the slow-varyingoptical mask, into a second electrical signal. The third channelincludes (i) a third lens for directing a third portion of the opticalsignal toward a fast-varying optical mask having a spatially-varyingtransmissivity T₃(x) having a same value at more than one value of x inthe x-range, and (ii) a third photodetector for converting the thirdportion, transmitted through the fast-varying optical mask, into a thirdelectrical signal. The microprocessor may be further configured to (i)determine a second and third frequency-domain amplitude from the second,and third electrical signals, respectively, and (ii) determine alocalization parameter of the object by comparing the first, second, andthird frequency-domain amplitudes.

(B6) In any localization system denoted by (B5), the microprocessor maybe further configured to execute steps (ii) through (vi) of the methoddenoted by (A6).

(B7) In any localization system denoted by (B6), the microprocessor maybe further configured to execute steps (i) through (iv) of the methoddenoted by (A7).

(C1) A localization system for determining a localization parameter ofan object includes a receiver and a signal processor. The receiverincludes a first channel, a second channel, and a third channel. Thefirst channel includes (i) a first lens for receiving a first portion ofan optical signal from the object and (ii) a first photodetector forconverting the received first portion into a first electrical signal.The second channel includes (i) a second lens for directing a secondportion of the optical signal toward a slow-varying optical mask havinga strictly monotonic transmissivity T₂(x) in an x-range of a spatialdimension x and (ii) a second photodetector for converting the secondportion, transmitted through the slow-varying optical mask, into asecond electrical signal. The third channel includes (i) a third lensfor directing a third portion of the optical signal toward afast-varying optical mask having a spatially-varying transmissivityT₃(x) having a same value at more than one value of x in the x-range,and (ii) a third photodetector for converting the third portion,transmitted through the fast-varying optical mask, into a thirdelectrical signal. The signal processor is configured to (i) determinefirst, second, and third signal amplitudes from the first, second, andthird electrical signals, respectively, and (ii) determine thelocalization parameter by comparing the first, second, and third signalamplitudes.

(C2) In the localization system denoted by (C1), the optical signal maybe a modulated optical signal having a modulation frequency, in whichthe first, second, and third signal amplitudes being a respective first,second, and third frequency-domain amplitude, corresponding to themodulation frequency, of the first, second, and third electricalsignals.

(C3) In a localization system denoted by one of (C1) and (C2), each ofthe first, second, and third channels may have a respective field ofview that overlaps with a field of view of both other channels.

(C4) A localization system denoted by one of (C1) through (C3) mayfurther include a uniform optical mask between the first photodetectorand the first lens and having a uniform transmissivity that equals orexceeds a maximum transmissivity of the slow-varying optical mask and amaximum transmissivity of the fast-varying optical mask.

(C5) In a localization system denoted by one of (C1) through (C4), thesignal processor may be configured to determine the localizationparameter by (i) determining a coarse-estimate location x₂ in thex-range and corresponding to a position on the slow-varying optical maskhaving transmissivity equal to the second signal amplitude divided bythe first signal amplitude, (ii) determining a plurality of candidatelocations {x_(3,1), x_(3,2), x_(3,3), . . . , x_(3,n)} in the x-rangeand corresponding to positions on the fast-varying optical mask havingtransmissivity equal to the third signal amplitude divided by the firstsignal amplitude, (iii) determining a refined-estimate location, of theplurality of candidate locations, closest to coarse-estimate locationx₂; and (iv) determining, based on the refined-estimate location, anangle of the object with respect to a plane perpendicular to the spatialdimension x and intersecting the masks.

(C6) A localization system denoted by one of (C1) through (C5) mayfurther include an emitter for at least one of (i) emitting and (ii)reflecting the optical signal, the emitter being located either (a) onthe object or (b) proximate the receiver and configured to direct theoptical signal at least toward a reflector mounted on the object.

(C7) In a localization system denoted by one of (C1) through (C6), theoptical signal may have a free-space wavelength between 0.40 micrometersand 2.0 micrometers.

(C8) In a localization system denoted by one of (C1) through (C7), thespatially-varying transmissivity T₃(x) may be a periodic function of x.

(C9) In a localization system denoted by one of (C1) through (C8), aportion of the slow-varying mask and a portion of the fast-varying maskmay be collinear along a line perpendicular to the x-dimension.

(C10) In a localization system denoted by one of (C1) through (C9), inwhich (a) the slow-varying optical mask spanning the x-range in spatialdimension x and spanning first y-range in a spatial dimension yorthogonal to spatial dimension x, and (b) the fast-varying optical maskspanning the x-range in spatial dimension x and spanning a secondy-range in spatial dimension y, transmissivity T₂(x) and transmissivityT₃(x) may be independent of y.

(C11) In a localization system denoted by one of (C1) through (C10), inwhich spatially-varying transmissivity T₃(x) is a periodic functionhaving a period Λ_(x), the receiver may further include a fourthchannel. The fourth channel includes (i) a fourth lens for receiving afourth portion of the optical signal toward a second fast-varyingoptical mask having a spatially-varying transmissivityT₄(x)=T₃(x+Δ_(x)), Δ_(x)≤0.5Λ_(x), and (ii) a fourth photodetector forconverting the fourth portion, transmitted through the secondfast-varying optical mask, into a fourth electrical signal. The signalprocessor is configured to (i) determine a fourth signal amplitude fromthe fourth electrical signals, and (ii) determine the localizationparameter by comparing the first, second, third, and fourth signalamplitudes.

(D1) A method for determining a localization parameter of an objectincludes steps 1-10. In step 1, the method directs a first portion of amodulated optical signal from the object. In step 2, the methoddetermines a first signal amplitude of the received first portion. Instep 3, the method directs a second portion of the modulated opticalsignal toward a slow-varying optical mask having a strictly monotonictransmissivity T₂(x), in an x-range of a spatial dimension x. In step 4,the method determines a second signal amplitude of the second portiontransmitted through the slow-varying optical mask. In step 5, the methoddirects a third portion of the modulated optical signal toward afast-varying optical mask having a spatially-varying transmissivityT₃(x) having a same value at more than one value of x in the x-range. Instep 6, the method determines a third signal amplitude of the thirdportion transmitted through the fast-varying optical mask. In step 7,the method determines a coarse-estimate location x₂ in the x-range andcorresponding to a location on the slow-varying optical mask havingtransmissivity equal to the second signal amplitude divided by the firstsignal amplitude. In step 8, the method determines a plurality ofcandidate locations {x_(3,1), x_(3,2), x_(3,3), . . . , x_(3,n)} in thex-range and corresponding to locations on the fast-varying optical maskhaving transmissivity equal to the third signal amplitude divided by thefirst signal amplitude. In step 9, the method determines arefined-estimate location, of the plurality of candidate locations,closest to coarse-estimate location x₂. In step 10, the methoddetermines, based on the refined-estimate location, an angle of theobject with respect to a plane perpendicular to the spatial dimension xand intersecting the masks.

(D2) In the method denoted by (D1), the step of directing the firstportion may include directing the first portion toward a uniform opticalmask having a uniform transmissivity that equals or exceeds a maximumtransmissivity of the second optical mask.

(D3) In a method denoted by one of (D1) and (D2), the optical signal maybe a modulated optical signal having a modulation frequency and acorresponding frequency-domain amplitude. The steps of determining thefirst, second, and third signal amplitude may further include:generating a first, second, and third frequency-domain representation ofthe first portion, the second portion, and the third portion,respectively; determining, as the first, second, and third signalamplitude, the frequency-domain amplitude of the first, second, andthird frequency-domain representation, respectively.

(E1) A repositionable mechanical structure includes a repositionablecomponent, an emitter, a controller, and an actuator. The emitter islocated on the repositionable component and is configured to emit anoptical signal to a receiver. The controller is adapted to receive acontrol signal from a transmitter communicatively coupled to thereceiver. The actuator is communicatively coupled to the controller andmechanically coupled to the repositionable component and is configuredto actuate the repositionable component based on the control signal.

(E2) The repositionable mechanical structure denoted by (E1) may furtherinclude the receiver. The receiver includes a first channel, a secondchannel, and a third channel. The first channel includes (i) a firstlens for receiving a first portion of an optical signal from the object,and (ii) a first photodetector for converting the received firstportion, into a first electrical signal. The second channel includes (i)a second lens for directing a second portion of the optical signaltoward a slow-varying optical mask having a strictly monotonictransmissivity T₂(x) in an x-range of a spatial dimension x, and (ii) asecond photodetector for converting the second portion, transmittedthrough the slow-varying optical mask, into a second electrical signal.The third channel includes (i) a third lens for directing a thirdportion of the optical signal toward a fast-varying optical mask havinga spatially-varying transmissivity T₃(x) having a same value at morethan one value of x in the x-range, and (ii) a third photodetector forconverting the third portion, transmitted through the fast-varyingoptical mask, into a third electrical signal.

(E3) The repositionable mechanical structure denoted by (E2) may furtherinclude a signal processor configured to (i) determine first, second,and third signal amplitudes from the first, second, and third electricalsignals, respectively, and (ii) determine a localization parameter ofthe emitter by comparing the first, second, and third signal amplitudes.

(E4) In the repositionable mechanical structure denoted by (E3), thesignal processor may determine the localization parameter by: (i)determining a coarse-estimate location x₂ in the x-range andcorresponding to a position on the slow-varying optical mask havingtransmissivity equal to the second signal amplitude divided by the firstsignal amplitude, (ii) determining a plurality of candidate locations{x_(3,1), x_(3,2), x_(3,3), . . . , x_(3,n)} in the x-range andcorresponding to positions on the fast-varying optical mask havingtransmissivity equal to the third signal amplitude divided by the firstsignal amplitude, (iii) determining a refined-estimate location, of theplurality of candidate locations, closest to coarse-estimate locationx₂; and (iv) determining, based on the refined-estimate location, anangle of the object with respect to a plane perpendicular to the spatialdimension x and intersecting the masks.

(E5) In a repositionable mechanical structure denoted by one of (E3) and(E4), the optical signal may be a modulated optical signal having amodulation frequency and a corresponding frequency-domain amplitude. Thesteps of determining the first, second, and third signal amplitude mayfurther include: generating a first, second, and third frequency-domainrepresentation of the first portion, the second portion, and the thirdportion, respectively; determining, as the first, second, and thirdsignal amplitude, the frequency-domain amplitude of the first, second,and third frequency-domain representation, respectively.

A method for determining a first frequency-domain amplitudecorresponding to a temporal frequency of a baseband signal is denoted by(F1). The method includes generating a plurality of estimates of thefirst frequency-domain amplitude. Each of the plurality of estimatescorresponds to a respective one of a plurality of temporal segments ofthe baseband signal. The method also includes determining the firstfrequency-domain amplitude as most common value of the plurality ofestimates.

(F2) In the method denoted by (F1), the step of determining the firstfrequency-domain amplitude may include (i) binning the plurality ofestimates into a plurality of bins, each of the plurality of binscorresponding to a respective interval between a maximum of theplurality of estimates and a minimum of the plurality of estimates, and(ii) determining the first frequency-domain amplitude as an estimatewithin one of the bins that corresponds to the interval having thegreatest number of estimates.

(F3) In the method denoted by (F2), the plurality of bins may include(i) a first plurality of bins corresponding to a first plurality ofintervals each with a respective center and a respective edge, and (ii)a second plurality of bins corresponding to a second plurality ofintervals shifted with respect to the first plurality of intervals suchthat a center of each of the second plurality of intervals correspondsto an edge of one of the first plurality of intervals.

(F4) Any method denoted by (F2), may further include, before the step ofgenerating a plurality of estimates, pre-processing the baseband signalusing a temporal differencing algorithm.

(F5) Any method denoted by one of (F1) through (F4) my further include(i) detecting a first portion of an optical signal from an object, theoptical signal being modulated at the temporal frequency, (ii) detectinga second portion of the optical signal transmitted through aslow-varying optical mask having a strictly monotonic transmissivityT₂(x), in an x-range of a spatial dimension x, (iii) detecting a thirdportion of the optical signal transmitted through a fast-varying opticalmask having a spatially-varying transmissivity T₃(x) having a same valueat more than one value of x in the x-range, and (iv) demodulating one ofthe detected first portion, the detected second portion, and thedetected third portion to yield the baseband signal.

(F6) Any method denoted by (F5), in which the one of the detected firstportion, the detected second portion, and the detected third portion isthe detected first portion, may further include (i) demodulating thedetected second portion to yield a second baseband signal, (ii)generating a second plurality of estimates, of a second frequency-domainamplitude corresponding to the temporal frequency, each corresponding toa respective one of a plurality of second temporal segments of thesecond baseband signal, (iii) determining the second frequency-domainamplitude as most common value of the second plurality of estimates,(iv) demodulating the detected third portion to yield a third basebandsignal, (v) generating a third plurality of estimates, of a thirdfrequency-domain amplitude, corresponding to the temporal frequency,each corresponding to a respective one of a plurality of third temporalsegments of the third baseband signal, and (vi) determining the thirdfrequency-domain amplitude as most common value of the third pluralityof estimates.

(F7) Any method denoted by (F6) may further include (i) determining acoarse-estimate location x₂ in the x-range and corresponding to alocation on the slow-varying optical mask having transmissivity equal tothe second frequency-domain amplitude divided by the firstfrequency-domain amplitude, (ii) determining a plurality of candidatelocations {x_(3,1), x_(3,2), x_(3,3), . . . , x_(3,n)} in the x-rangeand corresponding to locations on the fast-varying optical mask havingtransmissivity equal to the third frequency-domain amplitude divided bythe first frequency-domain amplitude, (iii) determining arefined-estimate location, of the plurality of candidate locations,closest to coarse-estimate location x₂, and (iv) determining, based onthe refined-estimate location, an angle of the object with respect to aplane perpendicular to the spatial dimension x and intersecting theslow-varying optical mask and the fast-varying optical mask.

(G1) A frequency-domain analyzer includes a memory and a microprocessor.The memory stores non-transitory computer-readable instructions and isconfigured to store a baseband signal having a temporal frequencycomponent and a corresponding first frequency-domain amplitude. Themicroprocessor is adapted to execute the instructions to: (i) generate aplurality of estimates of the first frequency-domain amplitude, whereineach of the plurality of estimates corresponds to a respective one of aplurality of temporal segments of the baseband signal, and (ii)determine the first frequency-domain amplitude as most common value ofthe plurality of estimates. Localization system 3300 of FIG. 33 mayfunction as the frequency-domain analyzer denoted by (G1)

(G2) In the frequency-domain analyzer denoted by (G1) the microprocessormay be further adapted to execute the instructions, when determining thefirst frequency-domain amplitude, to: (i) bin the plurality of estimatesinto a plurality of bins, each of the plurality of bins corresponding toa respective interval between a maximum of the plurality of estimatesand a minimum of the plurality of estimates, and (ii) determine thefirst frequency-domain amplitude as an estimate within the bincorresponding to the interval having the greatest number of estimates.

(G3) In the frequency-domain analyzer denoted by (G2), the plurality ofbins may include (i) a first plurality of bins corresponding to a firstplurality of intervals each with a respective center and a respectiveedge, (ii) a second plurality of bins corresponding to a secondplurality of intervals shifted with respect to the first plurality ofintervals such that a center of each of the second plurality ofintervals corresponds to an edge of one of the first plurality ofintervals.

(G4) In any frequency-domain analyzer denoted by one of (G2) and (G3),the microprocessor may be further adapted to execute the instructionsto, before the step of generating a plurality of estimates: pre-processthe baseband signal using a temporal differencing algorithm.

(G5) Any frequency-domain analyzer denoted by one of (G1) through (G4)may further include: (i) a receiver including a first channel, a secondchannel, and a third channel. The first channel includes (i) a firstlens for receiving a first portion of an optical signal from the object,and (ii) a first photodetector for converting the received firstportion, into a first electrical signal having the firstfrequency-domain amplitude, the optical signal being modulated at thetemporal frequency. The second channel includes (i) a second lens fordirecting a second portion of the optical signal toward a slow-varyingoptical mask having a strictly monotonic transmissivity T₂(x) in anx-range of a spatial dimension x, and (ii) a second photodetector forconverting the second portion, transmitted through the slow-varyingoptical mask, into a second electrical signal. The third channelincludes (i) a third lens for directing a third portion of the opticalsignal toward a fast-varying optical mask having a spatially-varyingtransmissivity T₃(x) having a same value at more than one value of x inthe x-range, and (ii) a third photodetector for converting the thirdportion, transmitted through the fast-varying optical mask, into a thirdelectrical signal. The microprocessor may be further configured to (i)determine a second and third frequency-domain amplitude from the second,and third electrical signals, respectively, and (ii) determine alocation parameter of the object by comparing the first, second, andthird frequency-domain amplitudes.

(G6) In any frequency-domain analyzer denoted by (G5), themicroprocessor may be further configured to execute steps (ii) through(vi) of the method denoted by (F6).

(G7) In any frequency-domain analyzer denoted by (G6), themicroprocessor may be further configured to execute steps (i) through(iv) of the method denoted by (F7).

Changes may be made in the above methods and systems without departingfrom the scope hereof. It should thus be noted that the matter containedin the above description or shown in the accompanying drawings should beinterpreted as illustrative and not in a limiting sense. The followingclaims are intended to cover all generic and specific features describedherein, as well as all statements of the scope of the present method andsystem, which, as a matter of language, might be said to falltherebetween.

What is claimed is:
 1. A method for determining a localization parameterof an object, comprising: detecting a first portion of an optical signalfrom the object, the optical signal including a baseband signalmodulated at a first temporal frequency; detecting a second portion ofthe optical signal transmitted through a first optical mask having afirst spatially-varying transmissivity and at least three firsttransmissivity values; detecting a third portion of the optical signaltransmitted through a second optical mask having a secondspatially-varying transmissivity that differs from the firstspatially-varying transmissivity and has at least three secondtransmissivity values; demodulating one of the first portion, the secondportion, and the third portion to recover the baseband signal;generating a plurality of estimates of a first frequency-domainamplitude of the baseband signal, each of the plurality of estimatescorresponding to a respective one of a plurality of temporal segments ofthe baseband signal, the first frequency-domain amplitude correspondingto the temporal frequency; binning the plurality of estimates into aplurality of bins, each of the plurality of bins corresponding to arespective one of a first plurality of intervals between a maximum ofthe plurality of estimates and a minimum of the plurality of estimates;determining the first frequency-domain amplitude as the estimate of theplurality of estimates that corresponds to the interval, of the firstplurality of intervals, having the greatest number of estimates; anddetermining the localization parameter based on the firstfrequency-domain amplitude, the localization parameter being at leastone of (i) an angle with respect to a receiver configured to detect thebaseband signal and (ii) a distance between the object and the receiver.2. The method of claim 1, the plurality of bins including (i) a firstplurality of bins corresponding to a first subplurality of intervals, ofthe first plurality of intervals, each with a respective center and arespective edge, (ii) a second plurality of bins corresponding to asecond subplurality of intervals, of the first plurality of intervals,shifted with respect to the first subplurality of intervals such that acenter of each of the second subplurality of intervals corresponds to anedge of one of the first subplurality of intervals.
 3. The method ofclaim 2, further comprising, before generating the plurality ofestimates, pre-processing the recovered baseband signal using a temporaldifferencing algorithm.
 4. The method of claim 1, when detecting thesecond portion of the optical signal, the first spatially-varyingtransmissivity being a strictly monotonic transmissivity T₂(x), in anx-range of a spatial dimension x; when detecting the third portion ofthe optical signal, the second spatially-varying transmissivity being aspatially-varying transmissivity T₃(x) having a same value at more thanone value of x in the x-range.
 5. The method of claim 1, the one of thedetected first portion, the detected second portion, and the detectedthird portion being the detected first portion, and further comprising:demodulating the detected second portion to yield a second basebandsignal; generating a second plurality of estimates, of a secondfrequency-domain amplitude corresponding to the temporal frequency, eachcorresponding to a respective one of a plurality of second temporalsegments of the second baseband signal; binning the second plurality ofestimates into a second plurality of bins, each of the plurality of binscorresponding to a respective one of a second plurality of intervalsbetween a maximum of the second plurality of estimates and a minimum ofthe second plurality of estimates; determining the secondfrequency-domain amplitude as the estimate of the second plurality ofestimates that corresponds to the interval, of the second plurality ofintervals, having the greatest number of estimates; demodulating thedetected third portion to yield a third baseband signal; generating athird plurality of estimates, of a third frequency-domain amplitude,corresponding to the temporal frequency, each corresponding to arespective one of a plurality of third temporal segments of the thirdbaseband signal; and binning the third plurality of estimates into athird plurality of bins, each of the plurality of bins corresponding toa respective one of a third plurality of intervals interval between amaximum of the third plurality of estimates and a minimum of the thirdplurality of estimates; determining the third frequency-domain amplitudeas the estimate of the third plurality of estimates and within one ofthe third plurality bins that corresponds to the interval, of the thirdplurality of intervals, having the greatest number of estimates.
 6. Alocalization system for determining a localization parameter of anobject comprising: a receiver including: a first channel including (i) afirst lens for receiving a first portion of an optical signal from theobject, and (ii) a first photodetector for converting the received firstportion into a first electrical signal having the first frequency-domainamplitude, the optical signal including a baseband signal modulated at afirst temporal frequency; a second channel including (i) a second lensfor directing a second portion of the optical signal toward aslow-varying optical mask having first spatially-varying transmissivity,and (ii) a second photodetector for converting the second portion,transmitted through the slow-varying optical mask, into a secondelectrical signal; a third channel including (i) a third lens fordirecting a third portion of the optical signal toward a fast-varyingoptical mask having a second spatially-varying transmissivity thatdiffers from the first spatially-varying transmissivity, and (ii) athird photodetector for converting the third portion, transmittedthrough the fast-varying optical mask, into a third electrical signal; amemory storing non-transitory computer-readable instructions andconfigured to store the baseband signal that includes the first temporalfrequency and, corresponding thereto, the first frequency-domainamplitude; and a microprocessor adapted to execute the instructions to:generate a plurality of estimates of the first frequency-domainamplitude, wherein each of the plurality of estimates corresponds to arespective one of a plurality of temporal segments of the basebandsignal; bin the plurality of estimates into a plurality of bins, each ofthe plurality of bins corresponding to a respective one of a firstplurality of intervals between a maximum of the plurality of estimatesand a minimum of the plurality of estimates; and determine the firstfrequency-domain amplitude as an estimate within one of the pluralitybins that corresponds to the interval, of the first plurality ofintervals, having the greatest number of estimates; and determine thelocalization parameter based on the first frequency-domain amplitude. 7.The localization system of claim 6, the plurality of bins including (i)a first plurality of bins corresponding to a first subplurality ofintervals, of the first plurality of intervals, each with a respectivecenter and a respective edge, (ii) a second plurality of binscorresponding to a second subplurality of intervals, of the firstplurality of intervals, shifted with respect to the first subpluralityof intervals such that a center of each of the second subplurality ofintervals corresponds to an edge of one of the first subplurality ofintervals.
 8. The localization system of claim 6, the microprocessorbeing further adapted to execute the instructions to, before the step ofgenerating a plurality of estimates: pre-process the baseband signalusing a temporal differencing algorithm.
 9. The localization system ofclaim 6, the first spatially-varying transmissivity being a strictlymonotonic transmissivity T₂(x) in an x-range of a spatial dimension x;the second spatially-varying transmissivity being a spatially-varyingtransmissivity T₃ (x) having a same value at more than one value of x inthe x-range; the microprocessor being further configured to (i)determine a second and third frequency-domain amplitude from the second,and third electrical signals, respectively, and (ii) determine alocalization parameter of the object by comparing the first, second, andthird frequency-domain amplitudes.
 10. The localization system of claim6, the microprocessor being further configured to: demodulate the secondportion to yield a second baseband signal; generate a second pluralityof estimates of a second frequency-domain amplitude, corresponding tothe temporal frequency, each corresponding to a respective one of arespective plurality of second temporal segments of the second basebandsignal; bin the second plurality of estimates into a second plurality ofbins, each of the plurality of bins corresponding to a respective one ofa second plurality of intervals between a maximum of the secondplurality of estimates and a minimum of the second plurality ofestimates; determine the second frequency-domain amplitude as theestimate of the second plurality of estimates that corresponds to theinterval, of the second plurality of intervals having the greatestnumber of estimates; demodulate the third portion to yield a thirdbaseband signal; generate a third plurality of estimates of a thirdfrequency-domain amplitude, corresponding to the temporal frequency,each corresponding to a respective one of a plurality of third temporalsegments of the third baseband signal; bin the third plurality ofestimates into a third plurality of bins, each of the plurality of binscorresponding to a respective one of a third plurality of intervalsbetween a maximum of the third plurality of estimates and a minimum ofthe third plurality of estimates; and determine the thirdfrequency-domain amplitude as the estimate of the third plurality ofestimates and within one of the third plurality bins that corresponds tothe interval, of the third plurality of intervals, having the greatestnumber of estimates.
 11. The localization system of claim 9, themicroprocessor being further configured to determine the localizationparameter by: determining a coarse-estimate location x₂ in the x-rangeand corresponding to a position on the slow-varying optical mask havingtransmissivity equal to the second frequency-domain amplitude divided bythe first frequency-domain amplitude; determining a plurality ofcandidate locations {x_(3,1), x_(3,2), x_(3,3), . . . , x_(3,n)} in thex-range and corresponding to positions on the fast-varying optical maskhaving transmissivity equal to the third frequency-domain amplitudedivided by the first frequency-domain amplitude; determining arefined-estimate location, of the plurality of candidate locations,closest to coarse-estimate location x₂; and determining the localizationparameter, based on the refined-estimate location, as an angle of theobject with respect to a plane perpendicular to the spatial dimension xand intersecting the slow-varying optical mask and the fast-varyingoptical mask.
 12. A frequency-domain analyzer comprising: a receiverincluding: a first channel including (i) a first lens for receiving afirst portion of an optical signal from the object, and (ii) a firstphotodetector for converting the received first portion into a firstelectrical signal having the first frequency-domain amplitude, theoptical signal including a baseband signal modulated at a first temporalfrequency; a second channel including (i) a second lens for directing asecond portion of the optical signal toward a slow-varying optical maskhaving first spatially-varying transmissivity, and (ii) a secondphotodetector for converting the second portion, transmitted through theslow-varying optical mask, into a second electrical signal; a thirdchannel including (i) a third lens for directing a third portion of theoptical signal toward a fast-varying optical mask having a secondspatially-varying transmissivity that differs from the firstspatially-varying transmissivity, and (ii) a third photodetector forconverting the third portion, transmitted through the fast-varyingoptical mask, into a third electrical signal; a memory storingnon-transitory computer-readable instructions and configured to storethe baseband signal that includes the first temporal frequency and,corresponding thereto, the first frequency-domain amplitude; theinstructions, when executed by a microprocessor, causing themicroprocessor to: generate a plurality of estimates of the firstfrequency-domain amplitude each corresponding to a respective one of aplurality of temporal segments of the baseband signal; bin the pluralityof estimates into a plurality of bins, each bin corresponding to arespective one of a first plurality of intervals between a maximum ofthe plurality of estimates and a minimum of the plurality of estimates;and determine the first frequency-domain amplitude an estimate withinone of the plurality of bins corresponding to the interval, of the firstplurality of intervals, having the greatest number of estimates.
 13. Thefrequency-domain analyzer of claim 12, the plurality of bins including(i) a first plurality of bins corresponding to a first subplurality ofintervals, of the first plurality of intervals, each with a respectivecenter and a respective edge, (ii) a second plurality of binscorresponding to a second subplurality of intervals, of the firstplurality of intervals, shifted with respect to the first subpluralityof intervals such that a center of each of the second subplurality ofintervals corresponds to an edge of one of the first subplurality ofintervals.
 14. The frequency-domain analyzer of claim 12, furthercomprising instructions that when executed by the microprocessor,further cause the microprocessor, before the step of generating aplurality of estimates: pre-process the baseband signal using a temporaldifferencing algorithm.
 15. The frequency-domain analyzer of claim 12,the first spatially-varying transmissivity being a strictly monotonictransmissivity T₂(x) in an x-range of a spatial dimension x; the secondspatially-varying transmissivity being the third channel including (i) athird lens for directing a third portion of the optical signal toward afast-varying optical mask having a spatially-varying transmissivityT₃(x) having a same value at more than one value of x in the x-range,and (ii) a third photodetector for converting the third portion,transmitted through the fast-varying optical mask, into a thirdelectrical signal; the instructions, when executed by themicroprocessor, further causing the microprocessor to (i) determine asecond and third frequency-domain amplitude from the second, and thirdelectrical signals, respectively, and (ii) determine a locationparameter of the object by comparing the first, second, and thirdfrequency-domain amplitudes.
 16. The frequency-domain analyzer of claim15, further comprising instructions, that when executed by themicroprocessor, further cause the microprocessor to: demodulate thesecond portion to yield a second baseband signal; generate a secondplurality of estimates of a second frequency-domain amplitude,corresponding to the temporal frequency, each corresponding to arespective one of a respective plurality of second temporal segments ofthe second baseband signal; bin the second plurality of estimates into asecond plurality of bins, each of the plurality of bins corresponding toa respective one of second plurality of intervals between a maximum ofthe second plurality of estimates and a minimum of the second pluralityof estimates; determine the second frequency-domain amplitude as theestimate of the second plurality of estimates and within one of thesecond plurality bins that corresponds to the interval, of the secondplurality of intervals, having the greatest number of estimates;demodulate the third portion to yield a third baseband signal; generatea third plurality of estimates of a third frequency-domain amplitude,corresponding to the temporal frequency, each corresponding to arespective one of a plurality of third temporal segments of the thirdbaseband signal; bin the third plurality of estimates into a thirdplurality of bins, each of the plurality of bins corresponding to arespective one of a third plurality of intervals between a maximum ofthe third plurality of estimates and a minimum of the third plurality ofestimates; and determine the third frequency-domain amplitude as theestimate of the third plurality of estimates and within one of the thirdplurality bins that corresponds to the interval, of the third pluralityof intervals, having the greatest number of estimates.
 17. Thefrequency-domain analyzer of claim 15, further comprising instructionsthat, when executed by the microprocessor, further cause themicroprocessor to determine the location parameter by: determining acoarse-estimate location x₂ in the x-range and corresponding to aposition on the slow-varying optical mask having transmissivity equal tothe second frequency-domain amplitude divided by the firstfrequency-domain amplitude; determining a plurality of candidatelocations {x_(3,1), x_(3,2), x_(3,3), . . . , x_(3,n)} in the x-rangeand corresponding to positions on the fast-varying optical mask havingtransmissivity equal to the third frequency-domain amplitude divided bythe first frequency-domain amplitude; determining a refined-estimatelocation, of the plurality of candidate locations, closest tocoarse-estimate location x₂; and determining, based on therefined-estimate location, an angle of the object with respect to aplane perpendicular to the spatial dimension x and intersecting theslow-varying optical mask and the fast-varying optical mask.